The 54-year-old has been given a 90-percent chance of beating the disease.
"I want to live. It is life you are talking about," Julien told the Trinidad Express newspaper. "I want to beat this thing. I am not giving up."
Julien, who also played English county cricket for Kent, was a left-arm fast bowler and respected right-hand batsman.
In his 24 Test match career, Julien claimed 50 wickets and scored 866 runs.
He also hit two Test centuries and was a member of the West Indian side that won the first World Cup in 1975.