In the general mathematical model, because some secondary factors should be ignored, the established model is often approximate, and the solutions of mathematical model obtained by numerical algorithm are mostly approximate solutions. On the other hand, in the case of non-compact feasible set, the set of accurate solutions is often empty, while in the weaker case, the set of approximate solutions can be nonempty. In Hausdorff locally convex topological linear spaces, the approximate Benson proper efficient solutions of unconstrained and constrained set-valued equilibrium problems are studied respectively. Without any convexity assumption, necessary and sufficient optimality conditions for approximate Benson proper efficient solutions are established by using nonlinear functional.