Maynard was born in Rockhampton, Queensland, and graduated from the University of Queensland. He spent a year as a resident master at Geelong Grammar School in Victoria, then joined the editorial staff of a Melbourne publisher. Despite the prevalent homophobia, Maynard dealt with homoerotic material in his poem 'Athlete', in the Bulletin (26 August 1959): 57, and in a short story, 'Conversations' in Westerly 3 (1959): 11-14.
Maynard read his poetry at the festival of Commonwealth poetry at the Royal Court Theatre, London in 1966 and has read at several Sydney Mardi Gras events. He was founding editor of New Guinea Writing, an advisory editor to Overland and contributing editor to Aspect. Maynard received an Australia Council Senior Writers' Fellowship in 1978. His poetry has appeared in many anthologies, such as Verse in Australia (1961), Australian Poetry (1964), Modern Australian Verse (1964), Australian Poetry Now (1970), The Penguin Book of Australian Verse (1972), New Guinea Images in Australian Literature (1982), Edge City (1983), Split Lips (1986), Made in Australia (1990), Love and Death (1987), Pink Ink (1991), Australian Gay and Lesbian Writing (1993), and Australian Poetry Today (1994).