Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A \oplus E$,the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equippedwith the algebras product $(a,x).(a^\prime,x^\prime)= (aa^\prime, a.x^\prime+ x.a^\prime)$. In this paper, we investigate $\triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$with the set of idempotents $E_S$, the module extension Banach algebra $S=l^1(E_S)\oplus l^1(S)$ is $\triangle$-amenable as a $l^1(E_S)$-module if and only if $l^1(E_S)$ is amenable as Banach algebra. تفاصيل المقالة