Founded by the amateur players of the Melbourne Symphony Orchestra in 1933, the orchestra remembers the contribution to Australian music of the former conductor and leader, Alberto Zelman. It has given at least three concerts each year since that time. Herbert Davis was the founding conductor. He was followed by Paul McDermott, then Leon La Gruta. Short-term guest conductors covered the next two years until Philip Carrington was appointed in 1980. He served as conductor of the orchestra from 1980 until 1999. Since 2000, the orchestra has worked under a number of conductors well known in Melbourne's amateur and professional music circles, including Philip Carrington, Phillip Green, Peter Handsworth, Gerald Keuneman, Janis Laurs, Rick Prakhoff, Tom Pugh, Joannes Roose and Mark Shiell. Mark Shiell was then appointed Principal Conductor & Artistic Director of the orchestra in 2010 and served in this capacity until 2017 when he left to focus once again on the flute. Rick Prakhoff commenced in the role in 2018. There have been only six appointed concertmasters of the orchestra: Bertha Jorgensen, Connie Ziebell, Donald Hancock, Yik Ming Chim, Mary Johnston and Susan Pierotti. Today the Zelman Memorial Symphony Orchestra comprises some 60 players in a full symphonic ensemble, performing classical, romantic and twentieth century symphonies and concertos with fine guest soloists. The orchestra performs four concerts a year in Melbourne, including the prestigious Piano Concerto Competition of the Boroondara Eisteddfod. In addition, the orchestra takes one or two concerts each year "on the road" to Victoria country locations that have included Daylesford, Drouin, Wendouree and Yea. The orchestra celebrated its 80th Anniversary in 2013–2014 with two performances to capacity audiences of Mahler's epic Eighth Symphony - the "Symphony of a Thousand" - at the Melbourne Town Hall. In what was believed to be "a first" for an Australian Community Orchestra, the performances involved over 580 performers including an augmented Zelman Symphony of some 125 players led by Guest Concertmaster, Wilma Smith, Concertmaster of the Melbourne Symphony Orchestra, and featuring many guest principal players from the MSO and other top orchestras and music institutions. David Macfarlane played the magnificent organ, a 370 voice choir was formed from nine community choirs, and an 80 voice children's choir involved students from Southern Voices and St Catherine’s School, Toorak.
The orchestra's celebrations concluded in grand style with a performance before an estimated 7,000 people at Melbourne's Sidney Myer Music Bowl on 22 February 2014. By invitation of the Melbourne Symphony Orchestra, the Zelman Symphony performed a program of Russian Favourites as a curtain raiser to the MSO's own performance later in the evening.