We define the notion of Johnson pseudo-contractibility for Banach algebras. We study this concept for some Banach algebras. For a compact metric space X and α > 0, we characterize Johnson pseudo contractibility of Lipschitz algebras. In fact, we show that Lipα(X) is Johnson pseudo-contractible if and only if X is finite. We give some examples to show the differences of Johnson pseudo-contractibility and other notions of amenability
