In this paper we introduce the new notion module Johnson amenability for a Banach algebra which is a Banach module over another Banach algebra with compatible actions. We study relations between this new notion to module pseudo amenability, module approximate amenability and also Johnson pseudo contractibility. We characterize the module Johnson amenability of ℓ1(S) as an ℓ1(E)-module, for an inverse semigroup S with subsemigroup E of idempotents. We investigate the module Johnson amenability of ℓ1(S), whenever S is Brandt semigroup or bicyclic semigroup or N with maximum as its product. We show that for every non-empty set I, MI (C) as an A-module under this new notion is forced to have a nite index, where A = { [ai;j ] 2 MI (C) j 8i ̸= j; ai;j = 0 } .
