Let B be any finite commutative ring with identity. In this case, · · · ⊂ B[X; 1 where p is a prime number and k ≥ 1, is the descending chain of commutative semigroup rings. All these semigroup rings are containing the polynomial ring B[X; Z 0 ]. In this paper, we introduced a construction technique of cyclic codes through the semigroup ring B[X; 1 p k Z 0 ] instead of a polynomial ring.