Zelinski was born in Southend-on-sea, Essex in August 1922. He joined the RAF as a teenager, serving as a pilot during the war, and meeting his wife, Mary, also serving in the air force.
He studied commercial art at Southend Art school, as part of a demob rehabilitation course. Moving to London he joined Carlton Artists around 1948, later turning freelance and using Artist Partners, Joan Farmer and Grestock and Marsh to secure commissions from magazines, publishers and ad agencies. Zelinski produced a prodigious number of illustrations for John Bull - a Sunday magazine, similar in style to the iconic American magazine The Saturday Post.
Zelinski’s work uses strong, bold colours, creating memorable images with a strong focus on characters and content. This graphic quality owes much to American illustrators. His works are distinguished by an almost photographic clarity and precision, although his use of colour brings them back into the world of painting. The colours are rich, flat, and vibrant, brilliantly evoking the optimism and energy of the time, and, perhaps, the character of the artist.
After living in London, Zelinski and his young family, moved to live in a Georgian house in Lewes, Sussex where he also worked. He was very fond of music and would spend the day listening to records and drawing. During his life he lived variously in some of the most beautiful parts of the English countryside, in Oxfordshire, Sussex, Dorset and Devon. After retiring from commercial work, he continued to draw and paint.