Badongo the silverback and his three female mates from Durrell Wildlife Park on Jersey were introduced to the musician's ceilidh hits by zoologist Jonathan Stark.
Mr Stark says they became hooked on the tunes of Sir Jimmy, who died in 2000 aged 92, after he played the music on his iPad.
He said: "They love new experiences and so I thought I would see what they made of Jimmy Shand.
"Let's say they loved it, and have taken a shine to accordion music."
The zoologist, who has worked at the park for six years, has built up such a rapport with the primates that they eat from his hand.
One of the animals has been trained to use a camera, while a female gorilla has learned to hold her arm out for regular contraceptive injections as part of the zoo's controlled breeding programme.