In this paper, we study the notion of Johnson pseudo-contractibility for certain Banach algebras. For a bicyclic semigroup S, we show that `1(S) is not Johnson pseudo-contractible. We give a necessary and sucient condition for a Fourier algebra to be Johnson pseudo-contractible. Also for a SIN-group G, we show that Johnson pseudo-contractibility of S1(G) is equivalent with amenability of G.