Given a C-dynamical system (A, G, $alpha$) with a locally compact group G, two kinds of C-algebras are made from it, called the full C-crossed product and the reduced C-crossed product. In this paper, we extend the theory of the classical C-crossed product to the C-dynamical system (A, G, $alpha$) with a left-cancellative semigroup M with unit. We construct a new C-algebra A $alpha$rM, the reduced crossed product of A by the semigroup M under the action $alpha$ and investigate some properties of A $alpha$rM.