He was born in Lucknow and then moved to Delhi with his family. Then lived in an area called Chitaranjan Park. Moitra shifted to Mumbai in 2002. He studied at Delhi University and has a degree in economics
Moitra composed music for Indipop albums that were hits including Mann ke Manjeere: an album of women's dreams for Breakthrough and Ab ke Saawan.
Moitra composed the music in a few films but gained recognition with his music in Pradeep Sarkar's Parineeta (2005). His music was critically acclaimed and he received a nomination for the Filmfare Best Music Director Award.
That same year he won the Filmfare RD Burman Award for New Music Talent.