Unmanned aerial vehicles (UAVs) are widely used to improve the coverage and communication quality of wireless networks and assist mobile edge computing (MEC) due to their flexible deployments. However, the UAV-assisted MEC systems also face challenges in terms of computation offloading and trajectory planning in the dynamic environment. This paper employs deep reinforcement learning to jointly optimize the computation offloading and trajectory planning for UAV-assisted MEC system. Specifically, this paper investigates a general scenario where multiple pieces of user equipment (UE) offload tasks to a UAV equipped with a MEC server to collaborate on a complex job. By fully considering UAV and UE movement, computation offloading ratio, and blocked relations, a joint computation offloading and trajectory optimization problem is formulated to minimize the maximum computational delay. Due to the non-convex nature of the problem, it is converted into a Markov decision process, and solved by the deep deterministic policy gradient (DDPG) algorithm. To enhance the exploration capability and stability of DDPG, the K-nearest neighbor (KNN) algorithm is employed, namely KNN-DDPG. Moreover, the prioritized experience replay algorithm, where the constant learning rate is replaced by the decaying learning rate, is utilized to enhance the converge. To validate the effectiveness and superiority of the proposed algorithm, KNN-DDPG is compared with the benchmark DDPG algorithm. Simulation results demonstrate that KNN-DDPG can converge and achieve 3.23% delay reduction compared to DDPG.