As the connecting hub of the airport runways and gates, the taxiway plays a very important role in the rational allocation and utilization of the airport resources. In this paper, a multi-strategy particle swarm and ant colony hybrid optimization algorithm, namely MPSACO is proposed to solve the airport runway planning problem and avoid taxiway conflicts and conflict propagation. Firstly, a reasonable mathematical model of airport taxiway planning is constructed. Secondly, the multi-strategy particle swarm optimization algorithm (CWBPSO) is employed to propose a new pheromone initialization approach for ACO. And a new pheromone allocation mechanism is designed and a new pheromone update strategy based on the principle of wolf predation is developed, which are combined to design a new pheromone hybrid strategy to enhance the pheromone influence of the optimal solution, dynamically adjust the search direction, and avoid to decline the best search ability, so as to greatly improve the optimization performance of the algorithm. Finally, an airport taxiway planning approach based on MPSACO is proposed, and a conflict adjustment strategy based on speed priority and the idea of first come and first serve (FCFS) is designed to effectively optimize the airport taxiway path. In order to prove the effectiveness of the proposed algorithm/method, 10 traveling salesman problems (TSP) with different scales and an actual airport taxiway planning problem are selected in here. The experiment results show that the proposed MPSACO can effectively solve TSP and obtain the better optimal solutions, and the proposed airport taxiway planning approach can effectively plan the airport taxiing path, avoid the airport taxiing conflicts, and improve the utilization rate of taxiway resources.