The pursuit-evasion game is a critical problem in artificial intelligence and draws a lot of attentions. In this article, we study the coordinated capture of multiple targets using multiple pursuers. A task allocation algorithm named distributed multitarget k-winners-take-all (DMK-WTA) is proposed for multiple evaders and multiple pursuers in this article, which is distributed and based on competition. In this algorithm, pursuers obtain hunting qualification through competition of task cost. After that, robots are controlled by predator-pack encirclement model (PPM), through which pursuers can automatically navigate to the target while avoiding collisions with obstacles and other robots. Combined with DMK-WTA and PPM, a distributed multitarget pursuit scheme in a dynamic environment has formed. By comparing with Kuhn-Munkres algorithm and genetic algorithm, we have evaluated the efficiency of DMK-WTA algorithm. Extensive simulations and physical experiments are conducted on a variety of robots to verify the viability and applicability of the proposed approach.