It is evening in Catfish Row, a former waterfront mansion that is now a Negro tenement, and its residents are involved in their usual nighttime activities. The young mother Clara sings a lullaby to her baby ("Summertime"). Serena tries to stop her husband, Robbins, from joining a crap game. Porgy, a kind crippled man, arrives and joins in the game. He dismisses the group's claims that he is in love with Bess, the girlfriend of a mean-tempered dockworker named Crown. Bess and Crown arrive together; the latter is drunk and joins in the crap game. A fight breaks out and Crown kills Robbins. He flees to avoid capture by the police, leaving Bess to fend for herself. Sportin' Life, the local drug peddler, approaches the shaken Bess and offers to take her to New York with him. She rejects him and unsuccessfully tries to find shelter with someone else in Catfish Row. Porgy open his door to her just as the police arrive.

Porgy, Bess, and the neighbors gather in Serena's home to pray over Robbins' body and everyone contributes money for his burial. A policeman investigating the murder accuses Peter, a honey peddler. When Peter says it was Crown who killed Robbins, the police take him into custody as a material witness. Serena mourns her loss ("My Man's Gone Now"). The undertaker, at first declaring that the $15 they collected is not enough, eventually agrees to bury Robbins and accept payment later. Bess leads the group in a spiritual ("Leavin' for the Promised Land").

Several weeks later, Jake and the other fishermen repair their nets in preparation to set out to sea ("It Takes a Long Pull to Get There"). In spite of his wife Clara's warning that September storms are on their way, Jake and his men are determined to go out on the water. Porgy appears and expresses the new-found joy that Bess's love has brought to his life ("I Got Plenty o' Nuttin'"). Maria, a shopkeeper, attacks Sportin' Life for peddling dope in front of her store. Frazier, a crooked lawyer, comes looking for Porgy and offers a "divorce" for Bess ("Woman to Lady"), claiming that the fact that she is not actually married to Crown makes the divorce even more expensive. A sympathetic white man, Mr. Archdale, appears and promises to get Peter out of jail. When a buzzard is seen overhead, it arouses Porgy's superstitious fears ("Buzzard Song"). Everyone makes preparations for a picnic on nearby Kittiwah Island but Bess is content to stay behind with Porgy ("Bess, You Is My Woman Now"). As the crowd heads off to the picnic, Porgy and Maria urge Bess to go and have a good time.

At the picnic on Kittiwah Island, Sportin' Life tells the group of the virtues of cynicism and his doubts on stories in the Bible ("It Ain't Necessarily So"). Serena is angered by his irreverence and denounces them all as sinners. She tells them that the boat is leaving soon and that they all must hurry to get on board. On her way to the boat, Bess is intercepted by Crown, who has been hiding out on the island. She tries to insist that she is now a respectable woman and living with Porgy, but he physically overcomes her and the boat goes without her.

Jake and his men leave on an extending fishing trip. Bess has arrived back at Catfish Row delirious after it took her several days to make her way back from the island. Peter returns from jail and, along with his wife Lily, Serena, and Porgy, he prays for Bess to get better ("Oh, Doctor Jesus"). Bess revives and Porgy tells her that he knows she has been with Crown, but that he forgives her. Bess assures him she wants to stay with him ("I Loves You, Porgy"), but she still fears Crown's power over her.

A terrible hurricane comes while the fishermen are still at sea and everyone gathers to pray for safety from the storm. Crown appears at the door and orders Bess to him. He mocks Porgy for being less than a man. When Jake's empty boat is seen outside, Clara runs out to try and find him. Crown rushes out after her and the others resume their prayers.

The storm is over and all of the inhabitants of Catfish Row are mourning Clara, Jake, and Crown, all of whom they assume are dead. Bess cares for Clara's baby in her absence. Suddenly Crown makes his way back to Porgy's door to claim Bess and in the ensuing fight, Porgy manages to kill him.

The police come to investigate Crown's murder but nobody will admit to seeing anything. They finally take Porgy with them to identify the body, despite his protests that he wants nothing to do with Crown. His reluctance is made worse when Sportin' Life suggests that Crown's body will start to bleed again in the presence of his killer. Once Porgy is gone, Sportin' Life seizes the opportunity to prey on Bess's fears of being left alone. He offers her some "happy dust" to soothe her nerves and suggests that she go with him to New York ("There's a Boat Dat's Leavin' Soon for New York"). She resists, but finally gives in, takes the "happy dust," and goes with him.

A week later Porgy returns home after his release from jail. When Bess doesn't come out to greet him and he sees Serena now caring for Clara's baby, he becomes worried ("Oh Bess, Oh Where's My Bess"). Serena and Maria explain to him what has happened, one excusing, the other condemning Bess for what she has done. Porgy resolves to go to New York to bring Bess back and leaves immediately on his journey ("Oh, Lawd, I'm on My Way").