In this paper, we study the existence and uniqueness of periodic solutions of the system of nonlinear neutral difference equations $\Delta x(n) = A(n) x(n-\tau(n)) + \Delta Q(n, x(n-g(n))) + G(n, x(n), x(n-g(n)))$. By using Krasnoselski's fixed point theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness. An example is given to illustrate our result. Our results extend and generalize the work [13].