In this paper, the existence of periodic solutions to a fourth-order nonlinear difference equation is studied. First, a variational functional corresponding to the difference equations as aforementioned is established. Next, the existence of periodic solutions can be simplified as the existence of critical point of the functional. By using critical point theory and some decomposition techniques of space, the sufficient conditions for the existence of a periodic solution are obtained. The practical effectiveness of our main theorem in view of an example is illustrated. Main results of this paper are helpful to enrich the theory of periodic solutions to fourth-order difference equations.