Let Γ be a k−regular graph with the second maximum eigenvalue λ. Then Γ is said o be Ramanujan graph if λ ≤ 2 √ k − 1. Let G be a finite group and Γ = Cay(G,S) be a Cayley graph related to G. The aim of this paper is to investigate the Ramanujan Cayley graphs of sporadic groups.