Let P(x) = xn + an−1x n−1 + .... + a1x + a0 be an irreducible polynomial over Fq. In [Cao, 2012, Varshamov, 1973, Lidl, 1987] the factorization of the composite polynomial P(x p − ax − δ), when a = 1 and T rFq/Fp (nb − an−1) = 0 is considered. The result of factorization of polynomial P(x p − x − δ) is a p irreducible polynomials of degree n over Fq. In this paper we propose an algorithm for factoring composite polynomial P(x p − x − δ) over Fq and give a explicit view of each factor.