In this paper we study Johnson pseudo-contractibility of second dual of some Banach algebras. We show that the semigroup algebra $\ell^{1}(S)^{**}$ is Johnson pseudo-contractible if and only if $S$ is a finite amenable group, where $S$ is an archimedean semigroup. We also show that the matrix algebra $M_{I}(\mathbb{C})^{**}$ is Johnson pseudo-contractible if and only if $I$ is finite. We study Johnson pseudo-contractibility of certain projective tensor product second dual Banach algebras.
