Amit Kumar was interested in music from an early age and he used to perform at Durga Puja celebrations. His father legendary Kishore Kumar introduced him to the world of acting while he was just 11 years old in his films Door Ka Rahi and Door Gagan Ki Chhao Mein. Famous song Aa Chalke Tujhe Me Dikhlau from the film Door Gagan Ki Chhao Me was picturised on him. He made his singing debut with a song in Door Ka Rahi.
For the first time in his career, he got an opportunity sing apart from his father’s production in the film, Darwaza and the song was Hosh Mein Hum Kahan. He garnered numerous accolades by singing RD Burman’s composed song "Bade Achchhe Lagte Hain" from the film Balika Badhu in the year 1976. He sang few duets with Lata Mangeshkar like "Dekh Mausam Keh Raha Hai" and "Uthe Sabke Kadam" and with Asha Bhosle sang a duet “Dhal Din Kaise”. All these songs garnered him national fame.
It was RD Burman who was instrumental in shaping his father’s career and he backed Amit and recorded around 170 Hindi songs with him. His career took off in the decade of 1980s and 1990s. Some of his songs such as Laila O Laila from Qurbani and Tirchi Topiwale of Tridev need a special mention. After 2000, he has sung very few songs. He sang "Naino Me Sapna” from the remake of film Himmatwala in 2013. The original song was sung by his father Kishore Kumar.
Besides Hindi, he has also sung in various other languages such as Marathi, Konkani, Bengali, Assamese, Oriya, and Bhojpuri.