In management or public decision making, there often exist two decision makers (DMs) in the situation where one of them has the priority in decision over another. Such decision making situations are often formulated as two-level programming problems. Under the assumption that these DMs know the objective function and constraints for the other DM and do not have motivation to cooperate mutually, the Stackelberg solution is adopted as a reasonable solution. However, for even two-level linear programming problems as the simplest case, the problem solved to obtain Stackelberg solutions is a nonconvex programming problem with complex structures and is known as an NP-hard problem. In this paper, we propose an efficient approximate solution method for two-level programming problems based on an evolutionary multi-agent system.