Summary: Let \(G\) be an abelian group with identity \(e\), \(R\) be a \(G\)-graded commutative ring and \(M\) a graded \(R\)-module where all modules are unital. Various generalizations of graded prime ideals have been studied. For example, a proper graded ideal \(I\) is a graded weakly (resp., almost) prime ideal if \(0\neq ab\in I\) (resp., \(ab\in I-I^{2}\)) implies \(a\in I\) or \(b\in I\). Throughout this work, we define that a proper graded submodule \(N\) of \(M\) is a graded almost prime if \(am \in N-(N:M)N\) implies \(a \in (N:M)\) or \(m\in N \). We show that graded almost prime submodules enjoy analogs of many of the properties of prime submodules.