Set in Dublin, Ireland in the year 1985, 15-year-old Conor Lalor (Ferdia Walsh-Peelo) is in his bedroom strumming his guitar. He overhears his parents Robert (Aiden Gillen) and Penny (Maria Doyle Kennedy) arguing, which he mimics in his song lyrics.
Conor joins his parents and siblings Brendan (Jack Reynor) and Ann (Kelly Thornton) down in the kitchen for a family meeting. Due to recent financial struggles, Robert announces that he and Penny are putting Conor in a free state school as opposed to paying for his current school. Brendan, a dropout/stoner, makes snarky comments regarding the situation.
Conor begins his new term at Synge Street CBS. He meets the school's principal, Brother Baxter (Don Wycherley), who tells him they have a strict black shoe policy, and Conor only owns brown ones. Conor later comes across the local bully Barry (Ian Kelly), who holds a slingshot at his face in the bathroom and forces him to dance. When he tells Conor to dance in his underwear, Conor refuses. During lunch, Conor buys a chocolate bar and gets it taken by Barry, who punches Conor in the eye. This leads to Conor meeting Darren (Ben Carolan).
As the two leave school, Conor spots a pretty girl across the street. Darren says she has no interest in any of the boys at school. Conor approaches her to say hello and introduces himself. She introduces herself as Raphina (Lucy Boynton), and she says she's a model. Conor asks her to be in a video for his band. Raphina asks him to sing a song. Not knowing anything, he sings two bars from "Take On Me" by a-Ha. Raphina agrees to be in the video. Conor then runs back to Darren and says they need to form a band.
Darren takes Conor to meet Eamon (Mark McKenna), a kid who is skilled at most instruments, but he settles on playing the bass guitar. Next, the boys recruit Ngig (Percy Chamburuka) to play the keyboard. Two more kids, Larry (Conor Hamilton) and Garry (Karl Rice), round out the band. Darren acts as the band's manager. They decide to call themselves "Sing Street". They first start by playing a cover of Duran Duran's "Rio". Conor plays it for Brendan, who says it's crap. He encourages his brother to write original songs to find their own style.
Inspired, Conor (with help from Eamon) writes the band's first original song, "The Riddle of the Model", which is obviously inspired by Raphina. He records a demo and gives a tape to Raphina so she knows what to expect for the video. The band later gathers to shoot the video for the song, with Raphina arriving to do make-up for the boys. Barry and his dad pass them, with the dad joking that Barry should join the band. When he tells his dad to piss off, he gets smacked in the face. After the shoot, Conor gives Raphina a ride home on his bike. He learns that she is seeing an adult man, and she lives at a home for girls since her parents are out of the picture.
Conor wears make-up to school and dyes the front of his hair blonde. Brother Baxter tells him to take the make-up off in his personal bathroom. When Conor leaves his office, Baxter grabs him and pulls him into the bathroom and violently washes the make-up off the boy.
After school, Conor meets up with Raphina and the boys to make another video for their song "A Beautiful Sea". Raphina also decides to call Conor "Cosmo" to fit with the band. The gang heads by the ocean for the shoot. Cosmo tells Raphina to pretend to jump into the water, but she does it for real, and he jumps after her when she says she can't swim. He then kisses her for the first time.
As Cosmo spends more time with Raphina, he learns that her dad died in a car accident, and her mom has been in and out of the local mental hospital for manic depression. She convinces Cosmo to lead his life as "happy-sad", meaning that it's okay to accept the "shittiness" in the world and go on with life and make art. Cosmo takes this philosophy to school when Barry threatens him again, but Cosmo coolly brushes him off and heads to class.
Cosmo, Darren, and Eamon see a sign at school for a dance where they can play a gig with the band. The boys all agree, and they get to rehearsing while also preparing for their midterms.
Cosmo goes to find Raphina and asks her to join him on an adventure. They take his grandfather's motorboat to Dalkey Island where they share tea and cookies. They spot the ferry headed to England. Cosmo then kisses Raphina again.
At home, Robert and Penny announce that they are splitting up, as Penny has fallen in love with her boss, citing Robert's neglect as a husband as one reason. She will be moving in with the boss, while Robert says he will get himself an apartment. Although it was expected, Brendan doesn't take the news well, telling Cosmo that he used to have ambitions to be someone, but has now resigned himself to being a stoner. He smashes his record player in anger.
The band practices the video for their song "Drive It Like You Stole It" at the gym in school. Cosmo looks for Raphina to show up, but she never does. In Cosmo's head, he imagines the video going like an American prom night with a 50's theme (like in the film "Back to the Future"). All the students are dancing, and Raphina shows up. Baxter does backflips across the floor. Robert and Penny show up, happily dancing and still in love. Brendan shows up with a neat haircut and tidy clothes. But the song ends, and Raphina still hasn't shown up.
Cosmo goes to the girls home to look for Raphina, but he is told by one of her housemates that she left the previous night to London with her boyfriend. Not long after, Cosmo spots Raphina returning to the home with a bruise on her cheek. The two go to the park where Raphina says that she left her boyfriend and he struck her, but she claims she deserved it. When she states that she might as well just work at a McDonald's and how she is just like her mother (no ambitions, hanging out with a schoolboy), Cosmo leaves her alone.
The night of the dance arrives, and the band wins over the other students. They have even gotten Barry to be their roadie. They play a great show until Cosmo says they will play a slow song. Most of the other students head to the back of the gym, but the couples dance together. For their final song, the band plays "Brown Shoes", which is for people like Baxter and all the other bullies the kids encounter. Cosmo hands out masks of Baxter's face to the other students. Raphina shows up as the band is playing the song to an excited crowd. Cosmo joins Raphina after the show.
The two run home to Brendan and convince him to drive them to their grandfather's boat so that Cosmo and Raphina can head out to London. Despite not knowing anyone, they will rely on Raphina's headshots and Cosmo's tapes and videos to get them some work. Brendan agrees to drive them there. Before leaving, Cosmo goes into his parents' room. Robert is sleeping on the floor. Cosmo tells his sleeping mother goodbye and that he loves her.
The three arrive by the ocean. Brendan says goodbye to his brother and tells Raphina to take care of him. As they leave, Brendan watches them ride away and cheers them on. It starts pouring rain, but the two manage to come across the ferry to England. With that, they proceed to follow it.