Path planning plays a crucial role in the execution of pursuit tasks for multiple unmanned ground vehicles (multi-UGVs). Although existing popular path-planning methods can achieve the pursuit goals, they suffer from some drawbacks such as long computation time and excessive path inflection points. To address these issues, this paper combines gradient descent and deep reinforcement learning (DRL) to solve the problem of excessive path inflection points from a path-smoothing perspective. In addition, the prioritized experience replay (PER) method is incorporated to enhance the learning efficiency of DRL. By doing so, the proposed model integrates PER, gradient descent, and a multiple-agent double deep Q-learning network (PER-GDMADDQN) to enable the path planning and obstacle avoidance capabilities of multi-UGVs. Experimental results demonstrate that the proposed PER-GDMADDQN yields superior performance in the pursuit problem of multi-UGVs, where the training speed and smoothness of the proposed method outperform other popular algorithms. As a result, the proposed method enables satisfactory path planning for multi-UGVs.