In this work, we study the existence of periodic solutions for some non-autonomous nonlinear partial functional differential equation of neutral type. We assume that the linear part is non-densely defined and generates an evolution family under the conditions introduced by N. Tanaka. The delayed part is assumed to be $\omega$-periodic with respect to the first argument. Using a fixed-point theorem for multivalued mapping, some sufficient conditions are given to prove the existence of periodic solutions. An example is shown to illustrate our results.