In this paper, we introduce a new unified family of polynomials including unified Apostol–Bernoulli, Euler and Genocchi polynomials, see Luo and Srivastava (2006) and a unified family of polynomials defined by Ozden et al. (2010). Also, by applying the Mellin transformation for the generating function of the new unified family of polynomials, we deduced a unified class of zeta function. Finally, we derive some relationships between our new unified family of polynomials and some types of generalized polynomials.