On a gangplank in New York City in 1933, glamorous passengers eagerly board the S.S. American, a luxury liner bound for England. Reporters aggressively photograph the passengers: Wall street executive Elisha J. Whitney; English gentleman Sir Evelyn Oakleigh; his fiancée, debutante Hope Harcourt; Hope’s overbearing mother, Mrs. Wadsworth Harcourt; Bishop Henry Dobson; two Chinese missionaries; and American evangelist-turned-nightclub singer Reno Sweeney, along with her four chorines, or “Angels.”
Whitney’s personal assistant, Billy Crocker, arrives to drop off his boss’s updated passport, and Whitney promptly fires him. Reno, who has known and adored Billy for years, invites him to sail with her as her new emcee (“You’re The Top”). Billy bumps into Hope and is stunned. Apparently, they shared a romantic evening months earlier, and Billy has been searching for Hope ever since. Billy immediately decides, with Reno’s help, to pursue Hope by stowing away on the ship. Gangster Moonface Martin, dressed as a preacher, enters with his girlfriend, Bonnie. They hop onboard just as Bishop Dobson is mistakenly arrested, and the ship sets sail (“Bon Voyage”). Billy, who inadvertently helped Moon board, takes the ticket and passport of Moon’s accomplice, Snake Eyes.
While Sir Evelyn is overcome by seasickness, Billy and Hope rekindle their romance (“It’s DeLovely”). The authorities think Billy is the real Snake Eyes, so Moon and Bonnie help disguise Billy in a sailor’s uniform (“Heaven Hop”). Reno joins the escapade by agreeing to distract Sir Evelyn. Reno, Billy, and Moon celebrate their partnership (“Friendship”). Reno flirts with Evelyn so Moon can catch them in a compromising position, and she realises she actually likes the Englishman (“I Get A Kick Out Of You”).
Billy manages to evade detection by donning a series of ridiculous disguises. When he’s finally found out, he's considered a celebrity, and the captain invites him for a drink. Hope is disappointed in Billy for being “a clown,” but Reno assures him things will work out (“Anything Goes”).
The passengers and crew honor Billy as “Public Enemy Number One,” and Bonnie leads a celebration (“Let’s Step Out”). Sir Evelyn and Reno get better acquainted (“Let’s Misbehave”) and Hope gets progressively more disgusted with Billy’s lie. Reno and Moon, still posing as a minister, perform a service to reform “Snake Eyes.” At the service, Evelyn confesses to a youthful tryst with a Chinese girl named Plum Blossom, Billy admits his deceit, and Reno leads a revival (“Blow, Gabriel, Blow”).
Billy and Moon are thrown in the brig. In jail, Billy can’t stop thinking about Hope (“All Through The Night”) so Moon attempts to cheer him up (“Be Like The Bluebird”). The two Chinese missionaries are also jailed for gambling. Hope visits Billy and they reaffirm their love (“All Through The Night” Reprise). Unfortunately, Mrs. Harcourt has arranged for Hope and Evelyn to marry in just a few hours. Billy and Moon come up with a plan; they begin a game of strip poker with the missionaries.
Meanwhile, Reno and the Angels miss life in New York (“Take Me Back To Manhattan”). Evelyn confesses he loves Reno, but he has to follow through on his commitment to marry Hope.
The wedding begins, but it’s soon interrupted by Billy and Moon, disguised as the two Chinese missionaries, along with Reno disguised as Plum Blossom. The three impostors manage to cancel the wedding, and soon Hope and Billy end up together, as do Reno and Sir Evelyn, Bonnie and Moon, and Mrs. Harcourt and Mr. Whitney. The captain receives a telegram from Washington saying Moonface Martin is “Not wanted. Entirely harmless. Wouldn’t hurt a flea.” Despite Moon’s bitter disappointment, the entire company celebrates together (Finale: “You’re The Top”).