In a recent paper by A. Ebadian and A.A. Shokri , a α-Lipschitz operator from a compact metric space X into a unital bounded commutative Banach algebra B is defined. Let (X,d) be a nonempty compact metric space, 0<α≤1 and (B, || . ||) be a unital bounded commutative Banach algebra. Let Lipα(X,B) be the algebra of all bounded continuous operators ƒ: X → B such that [formula/wzor]. In this work, we characterize the maximal ideal space of Lipα(X,B).