In this paper, we investigate the existence and uniqueness of (ω, Q) -periodic mild solutions for the following problem x′(t)=Ax(t)+f(t,x(t)), t∈R, on a Banach space X. Here, A is a closed linear operator which generates an exponentially stable C-semigroup and the nonlinearity f satisfies suitable properties. The approaches are based on the well-known Banach contraction principle. In addition, a sufficient criterion is established for the existence and uniqueness of (ω, Q) -periodic mild solutions to the Hopfield-type neural network model.