Computation offloading, resource allocation, and endurance issues in unmanned aerial vehicle (UAV)-aided mobile edge computing (MEC) networks have always been a research focus. UAV-aided MEC allows mobile users’ (MUs’) tasks to be offloaded to drones for processing in special scenarios, such as natural disasters or military attacks. However, as the number and size of offloaded tasks continuously increase, it is difficult for a single UAV to meet all computational demands, result in the decline of QoS. In order to address this issue, this paper presents a collaborative computation offloading scheme where multiple UAVs can cooperate to handle massive tasks. Firstly, considering that battery-limited UAVs cannot complete all tasks and sustain flight without recharging, we incorporate charging stations (CS) into multi-UAV-assisted MEC networks. Subsequently, we design a price-based incentive mechanism to encourage the adjacent UAVs with unused computation resources to cooperate with busy UAVs, so as to maximize the total revenue obtained from UAVs’ collaborative computation. Then, we formulate the joint optimization problem of computation offloading, resource allocation and charging scheduling as a Markov Decision Process (MDP), and propose a Twin Delayed Deep Deterministic policy gradient (TD3) algorithm to find optimal strategies. Finally, extensive simulations demonstrate that the proposed TD3 algorithm outperforms other benchmark methods, achieving the maximum overall system utility under different scenarios.