Elisha Whitney, a successful Ivy league Wall Street banker, waits impatiently for his assistant, Billy Crocker, to meet him at a New York City bar. Billy is to drop off some items Whitney needs for his vacation, and Whitney has to give Billy instructions to sell some stock for his personal account. It turns out that Billy forgot his boss' passport, so he will have to deliver it to Whitney on the cruise ship the following morning. Coincidence has it that Billy's old friend Reno Sweeny, a sexy Evangelist turned nightclub singer, plans to travel on the same boat as Whitney. Reno is interested in Billy romantically - I Get A Kick Out Of You, but Billy explains to her that he is in love with a girl named Hope. Reno even invites Billy to join her on the trip - There's No Cure Like Travel, but Billy just isn't interested in her that way.
Transatlantic voyages usually draw celebrities and, therefore, photographers. But Charlie Chaplin cancelled his plans on the ship at the last minute. This leaves Hope Harcourt, the American debutante to photograph. She is travelling with her fiancé Lord Evelyn Oakleigh, a wealthy Englishman and her mother Evangeline Harcourt, a widow. The photographers are not impressed by the Minister Henry T. Dobson and his two Chinese converts, but they take notice when Reno Sweeny and her four Showgirl Angels board the ship. Coincidence has it that Evangeline and Whitney are old friends.
When Billy boards the ship to drop off Whitney's passport, he finds out that his long lost love, Hope, is a passenger, and is to be married. As Billy tries to find Hope before the ship leaves the dock, two pushy F.B.I. agents force Billy to show them where the Minister is. Billy inadvertently identifies Minister Dobson as Moonface Martin, a gangster and Public Enemy #13, to the F.B.I. agents. Dobson is thrown in the ship's brig, and his two converts are allowed to wander the ship without supervision. Moonface and his friend Erma are indebted to Billy, and thank him by giving him their friend's unused ticket and room. The problem is that their friend who didn't make it on board is Snake Eyes Johnson, Public Enemy # 1, and wanted by the F.B.I. too. Now Billy is mistaken for Snake Eyes (Mr. Murray Hill Flowers on the ticket), and must disguise himself for the rest of the trip in order to stay out of jail. He must also stay out of Whitney's sight, because his boss specifically sent him off the ship and back to work. Billy thinks all this trouble is worth while, since he has the chance to convince Hope to fall in love with him.
Billy convinces Reno to help him win Hope's heart - You're The Top. After the ship leaves the dock, Billy is able to spend some time alone with Hope because Evelyn is seasick. He sings her Easy To Love. Billy goes so far as to disguise himself as a sailor with Erma's help. He convinces Evangeline Harcourt the boat is sinking, and convinces Whitney the whipped cream he throws on his glasses is from a seagull. Moon also helps Billy with his cause, by tricking Whitney and taking his glasses. Not only can Whitney not see Billy, but he can barely see anything during the whole trip. In fact in a funny scene, Whitney thinks he is proposing marriage to Evangeline and ends up asking the ship's Purser to marry him. Moon and Reno come up with a plan for Reno to seduce Evelyn, and break up Evelyn and Hope. Reno and Moon sing Friendship. Although the plan fails, Reno realizes she really likes Evelyn and is genuinely interested in him romantically.
At one point Billy disguises himself with a beard made of Evangeline's dog's hair. Minutes later Billy is dressed as a ludicrous version of an English gentleman, while Moon wears a white coat and carries a butterfly net. Billy and Moon try to convince Evangeline that her daughter is about to marry a crazy man, but Billy's true identity is revealed before they are able to convince Evangeline that Evelyn is crazy. Billy's next disguise is as an old lady in a wheelchair, and he sings It's De-Lovely with Hope.
The Purser finally catches Billy, who he thinks is Snake Eyes Johnson. But instead of being afraid of Snake Eyes, the passengers welcome him aboard and celebrate the criminal - Anything Goes. To get some attention himself, Moon confesses his true identity - Public Enemy Number One. Reno encourages Billy to pursue Hope. Moon uses his newfound notoriety to marry Reno's Angel, Virtue, in a fake ceremony. During Reno's Sermon/Nightclub act, many passengers confess to immoral behavior in the past. Evelyn is among the confessors, with the admission of an affair with a Japanese girl many years ago. Reno encourages more confessions with Blow, Gabriel, Blow, and Billy is next when he admits he is not really Snake Eyes and that he is on the ship to chase Hope. Billy and Moon are finally sent to the ship's brig, and Hope sings Goodbye, Little Dream, Goodbye sadly.
In jail Moon tries to cheer Billy up with Be Like The Blue Bird. Hope sends Billy a note, and they sing All Through The Night . Later that night Evelyn realizes and professes his love to Reno. He plans to carry out his obligation to Hope and marry her, though - The Gypsy In Me. The two Chinese converts run wild on the ship without Reverend Dobson's supervision, and finally get themselves thrown in the brig with Billy and Moon. Reno visits the men in jail, and tells them that she and Evelyn are in love with each other. Billy and Moon trick the two converts in a game of strip poker, and change clothes with them. Instead of the converts being released from jail, Billy and Moon are set free just in time to stop Hope's wedding to Evelyn
Erma opens the final scene with Buddy Beware. Reno joins Billy and Moon in their effort to break off the wedding. Reno pretends to be Evelyn's illegitimate daughter from the affair he confessed to during Reno's sermon. Evelyn is flustered by his unknown daughter's appearance, and almost lets Whitney pay her off to disappear. Hope stops this from happening by coming up with a plan to pay the debt of honor: to even the score Evelyn must offer Hope to Plum Blossom's relative, who is actually Billy. Now Hope and Billy, and Reno and Evelyn are together. Evangeline Harcourt is irate about this arrangement, because this means her daughter is not marrying a rich man. Whitney saves Evangeline's day by proposing, but she may end up like her daughter - in love but poor - because Billy never sold Whitney's stock for him. Whitney gets lucky and his stock goes through the roof. All three happy couples marry.