Aimming at the phenomenon that the discriminating theorem of discriminating domain of the general nonlinear system is difficult to be used, a bounded discriminating domain for linear pursuit-evasion differential games is studied. If a closed set is a discriminating domain of the differential games, the convex hull of the set is also a discriminating domain of the differential games. A polyhedral discriminating domain is obtained, and an efficient algorithm is given, which is easy to be used. By using the alternative theorem, the victory domain of the differential games can be obtained. An example is given to show the feasibility and effectiveness of the proposed algorithm.