In this work, we give sufficient conditions for the existence of periodic and positive periodic solutions for a nonlinear neutral mixed type Levin-Nohel integro-differential equation with variable delays by using Krasnoselskii's fixed point theorem. Also, we obtain the existence of a unique periodic solution of the posed equation by means of the contraction mapping principle. As an application, we give an example to illustrate our results. Previous results are extended and generalized.