In this work,  injective semimodule  has been generalized to  almost -injective semimodule. The aim of this research is  to study the basic properties of the concept almost- injective semimodules. The semimodule  is called  almost  -injective semimodule if, for each subsemimodule A of  and each homomorphism  : A   , either there exists  a homomorphism  such that = . Or there exists a homomorphism : Y such that = , where Y is nonzero direct summand of , and   is the  projection map. A semimodule  is almost injective semimodule if it is almost injective relative to all semimodules. Every injective semimodule is almost injective semimodule,  if  is almost  –injective semimodule and    is simple, then  is -injective.  In addition, some related concepts  it have been studied and investigated as well.