Abstract: The constraint conditions of successful capture in multi-robot 2D pursuit-evasion game with n pursuers and one evader are researched. Based on the theoretical analyses, under the condition that all robots have global visual field, the pursuers using appropriate strategy can always capture the evader, even if the top speed of the pursuers is lower than that of the evader when the following two conditions are both satisfied. One is that the speed ratio of each pursuer to the evader is higher than sin (π/n), and the other is that the evader should be located in the convex polygon which takes the multiple pursuers as vertexes, and that the adjacent Apollonius circles formed by the evader and each pursuer should be intersected or tangent. In addition, the pursuit-evasion strategies for pursuer and evader are designed under the proposed constraint conditions. Results of many simulation experiments can also prove that the constraint conditions are correct.