As a child, Alfred "Al" Yankovic becomes interested in parodying songs against his father's wishes. Al's mother secretly purchases an accordion for him, but his father destroys it when Al is caught at an illicit polka party, thus straining Al's relationship with his parents.

Living with his roommates Steve, Jim, and Bermuda, Al tries to join bands as an accordion player but is constantly rejected. While listening to "My Sharona" on the radio and fixing a bologna sandwich, Al is inspired to write "My Bologna". He sends the song to a local radio DJ, who puts it on the air immediately; he then goes to Scotti Brothers Records, where the brothers mock him, but are willing to reconsider if Al gains more experience.

Al performs "I Love Rocky Road" for the first time at a biker bar, his roommates stepping in to fill out his band and make the performance a success. Al catches the interest of Dr. Demento, who offers to be his manager while suggesting he go by the stage name "Weird Al". At a party hosted by Dr. Demento, the doctor's rival Wolfman Jack dares Al to prove himself by parodying Queen's "Another One Bites the Dust" with bassist John Deacon present; Al comes up with "Another One Rides the Bus", impressing the celebrities in attendance. Al lands his record contract, and his debut album goes multi-platinum, with the original artists getting a "Yankovic bump" in record sales and Al being feted by Oprah Winfrey.

Al calls home to find his father is still dismissive of him. Dr. Demento suggests Al try to make his own original song, which Al refuses. However, after Dr. Demento gives Al guacamole laced with LSD, he comes up with an original new song, which becomes his next hit, "Eat It". Madonna, in search of the "Yankovic bump", begins a relationship with Al to convince him to parody her song "Like a Virgin", though he insists he now only writes original songs. Dr. Demento and Al's bandmates warn him that Madonna is a bad influence, but they continue their romance. Just before a major show, Al learns that Michael Jackson has taken "Eat It" and parodied it as "Beat It", which angers him since he believes people will assume "Eat It" is a parody of "Beat It". An intoxicated Al suffers a near-fatal car accident and is rushed to the hospital, where he comes up with "Like a Surgeon" after regaining consciousness. He premieres the song at a show that same night, while still heavily injured, but when he is reminded that "Eat It" is the last song for the show, he gets drunk on stage, insults the crowd, and is arrested for lewdness.

Once released, Al confesses to Madonna that he fears he has alienated everybody who cared about him and that she is the only one he has left. Suddenly, Madonna is captured by agents of Pablo Escobar, who is a huge fan of Al and uses the kidnapping to coerce him to play at his fortieth birthday party. Al flies to Colombia and goes on a rampage to break into Escobar's compound, where he confronts the drug lord. After refusing to play a song for him, he gets into a shootout and kills Escobar and his mercenaries to free Madonna. With the kingpin dead, Madonna tries to talk Al into giving up music and helping her take over his drug empire, but Al rejects her.

Al returns home to work in his father's factory; Al's father admits that Al never belonged in that line of work and secretly supported Al's chosen path. The elder Yankovic reveals he grew up in an Amish community and was excommunicated for taking up the accordion, prompting h