The play opens on a rocky sea-shore on the coast of Cornwall, England, around 1880. The pirates are lounging about on this secluded spot having a birthday celebration for their young apprentice, Frederic, who has reached his 21st year ("Pour, O Pour the Pirate Sherry"). However, as Frederic is out of his indentures on this day, he has decided to go off into civilization and become an upstanding citizen, which also means that it will be his duty to bring the pirates to justice. His nurse maid, Ruth, who has helped to raise Frederic, reveals the truth that it was due to her hard-of-hearing that she accidentally apprenticed him to a pirate instead of a pilot ("When Frederic Was a Little Lad"). The Pirate King takes the news good-naturedly and wishes Frederic well, but refuses to turn himself in. He would rather live and die a pirate ("Oh, Better Far to Live and Die").

Ruth wishes to travel on with Frederic, perhaps even become his future wife. As Frederic has never known any other women, he asks the middle-aged Ruth if she is considered to be beautiful. Ruth swears that she is, but her story is found false as a gaggle of girls come hopping and skipping and singing down to the shore. They are all young and beautiful and finally, for the first time in his life, Frederic recognizes the beauty of youth ("Climbing Over a Rocky Mountain"). Frederic turns on Ruth and accuses her of playing upon his innocence ("Oh, False One").

Ruth runs off, upset and alone, but Frederic hides among the rocks to watch the girls approach. He decides that he'd better make his presence known ("Stop, Ladies, Pray!") and tries to explain that his pirate costume does not indicate that he is a criminal, but that he indeed wishes to become an upstanding citizen ("Oh, Is There Not One Maiden Here"). The sisters, all shocked by this young pirate, take the proper course and reject him. However, one sister, Mabel, arrives on the scene late and is taken with Frederic's noble goals ("Poor Wandering One!"). For Frederic and Mabel it is love at first sight, but the lovely scene is interrupted by the arrival of the attacking pirates ("Stay, We Must Not Lose Our Senses").

Just as all seems lost, the father of the girls arrives and happens to be a Major-General ("I Am the Very Model of a Modern Major-General"). Knowing that, historically, the Pirates of Penzance do not attack orphans, the General announces that he is an orphan in the hopes that the pirates will set his daughters free ("Oh, Men of Dark and Dismal Fate"). The Pirates feel sorry for the General and agree to let the daughters go free and, for the moment, all is happy.

Scene Two opens at the Major-General's castle at night. The Major-General cannot sleep and is wandering the grounds, upset. His daughters come out to comfort him ("Oh, Dry the Glistening Tear"). The General tells Frederic that he escaped from the pirates because he said he was an orphan, but it wasn't true. He fears the pirates will find out and come to attack him again. Frederic has organized the police force to overtake the pirates and feels the General has nothing to fear – the pirates will be in jail before midnight ("When the Foeman Bares His Steel").

Frederic, alone to ready himself for battle, receives a surprise visit from the Pirate King and Ruth. They come with unfortunate news: as Frederic was born on the 29th of February, his birthday only comes once every four years and therefore he is only five birthdays old. According to his indentures, he is to remain in the pirates' service until his 21st birthday ("When You Had Left Our Pirates' Fold"). Resigned to his duty, Frederic agrees to join the pirates in attacking the General for falsely claiming himself as an orphan. However, he swears to Mabel that he will return to her (even though it will be 1940) when he has completed his apprenticeship with the pirates.

The Police Sergeant must now lead his force alone ("Tarantara, Tarantara!"). Upon hearing the pirates approach, ("A Rollicking Band of Pirates We") the police force decides that the best measure of defense is to hide. The pirates arrive on the scene ready for battle ("With Cat-like Tread, Upon Our Prey We Steal"). Hearing the Major-General coming outside, the pirates decide to hide and ambush him. The daughters reappear to find out why the General is out of bed again ("Now What is This and What is That?"). The pirates attack, and the police force drums up the courage to save the daughters. A bold battle ensues, but the pirates are cut short when the Sergeant charges the pirates in the name of the Queen. The pirates, feeling duty to the Queen beyond all other infractions of the law, give themselves up. Ruth steps forward to explain to the Sergeant that the pirates are all noble men who have done wrong and deserve the chance to become upstanding citizens ("Finale"). Mabel and Frederic are reunited, and all the pirates become loyal subjects to the Queen.