Alberto Zelman (1874-1927), in whose memory the Orchestra was formed and named, founded the original Melbourne Symphony Orchestra in 1906. The MSO continued to perform after Alberto's death until 1932 when it was taken over by Professor (later Sir) Bernard Heinze who converted it to an all-professional orchestra. The amateur players formed their own orchestra in 1933, naming it the Zelman Memorial Symphony Orchestra after their beloved Alberto.

The current Zelman Memorial Symphony Orchestra comprises some 60 - 80 players in a full symphonic ensemble. The orchestra performs classical, romantic and twentieth century symphonies and concertos with fine guest soloists at each concert. They usually hold four concerts a year in Melbourne and one concert at a Victorian regional centre.

Rick Prakhoff was appointed Artistic Director in 2018.