By means of critical point theory, we investigate homoclinic solution problems for the Kirchhoff-type difference equations with periodic coefficients. First, we verify that the graph of the energy functional satisfies the mountain pass geometrical properties. Such mountain pass geometry produces a Palais-Smale sequence. Second, we exploit one global property condition to guarantee that this Palais-Smale sequence is bounded. Further, by using the subset of $l^{2}$ consisting of functions with compact support and periodicity of coefficients, we obtain the existence of one nontrivial homoclinic solution for the Kirchhoff-type difference equations with periodic coefficients. Finally, two examples are given to illustrate our main results.