In this paper, new generalizations of injective (projective) semimodules are introduced. Some of its characterizations are discussed, as well as some properties of quasi-injective and quasi-projective semimodules are extended for direct-injective (projective) semimodule. If a semimodule W is named direct-injective symbolize (Di-injective), if for any direct summand V of W, a monomorphism ∅:V→ W, there is a homomorphism α:W→ W such that α∅ = iv. A semimodule ℘ is said to be direct-projective symbolize (Di-projective), if for any direct summand U of ℘ with projection ν:℘→ U and epimorphism μ:℘→ U, there is an endomorphism α:℘→ ℘ such that μα=ν.