Melvin Steinberg attended the common schools and then studied until 1952 at the University of Baltimore. After a subsequent law degree from the same university in 1955 and was admitted to his lawyer, he began to work in this profession. Previously, he served from 1955 to 1957 in the U.S. Navy. Politically, he joined the Democratic Party. Between 1967 and 1987 he was a member of the Senate of Maryland, he served as Chairman since 1983. From 1975 to 1978, who there deputy chairman of the Judiciary Committee; between 1979 to 1982, he headed the Finance Committee. He was also during his time in the State Senate member and vice chairman of several other committees.
1986 Steinberg was elected on the side of William Donald Schaefer as Vice Governor of Maryland. This post he held for a re choice between 1987 and 1995. Doing so, he acted as deputy governor. He was also a member of numerous committees and associations. With Governor Schaefer there were occasional personal and political differences. In 1994 he applied unsuccessfully for his party's nomination for the office of governor. He then worked as a lobbyist.