This paper addresses a multi-agent Homicidal Chauffeur reach-avoid game, where M simple-motion evaders aim to reach the goal region, while N Dubins-car pursuers aim to prevent that by capturing evaders, and it is assumed that \(N \ge M\) and only incomplete information can be obtained by pursuers. We begin with one-pursuer-one-evader situation, and the optimal path types of the agents are inferred by the Hamiltonian of the differential game based on Homicidal Chauffeur dynamical model. Further, the optimal strategies of the agents are deduced from the engagement line we construct. Afterwards, the situation is expanded to two-pursuer-one-evader, where the intersection of engagement lines is introduced to describe the cooperation of two pursuers. Then, we analyze the N-pursuer-M-evader game by the combination of one-pursuer-one-evader and two-pursuer-one-evader games, and a potential game-based matching approach is proposed to achieve the combination with incomplete information. Simulation and reality experiments are provided to illustrate the theoretical results, where Joint Strategy Fictitious Play (JSFP) with inertia algorithm is executed to obtain the pure strategy Nash equilibrium. It is verified that the optimal pursuer-evader assignment is switchable and our scheme is feasible.