In this paper, we principally introduce the concept of quasi-principally k-flat semimodules, on the basis of the theories of k-flat semimodules and quasi-principally modules, we get some good properties of quasi-principally k-flat semimodules, therefore generalize some properties of quasi-principally modules of rings and k-flat semimodules of semiring to quasi-principally k-flat semimodules of semirings.

subtractive semimodules, k-regular homomorphism proper exact sequence, quasi-principally, k-flat semimodules, injective semimodules.