Abdur Rashid was born in 1937 to a Bengali family of Muslim Beparis in the village of North Nasruddi in Daudkandi, Tipperah District, Bengal Presidency (now Bangladesh).
Abdur Rashid passed his matriculation from Daudkandi High School in 1952, and ISC from Jagannath College in 1954.
Abdur Rashid began his career as an engineer for the Comilla District Board.
He left the Awami League in 1973, joining the National Socialist Party and being appointed president of the Comilla District Board.
He contested as an Awami League candidate at the February 1996 Bangladeshi general election but was unsuccessful yet again.