Unmanned aerial vehicle (UAV) is equipped with an edge server to constitute a mobile edge server. It can provide computing services for user equipment (UE) in some scenarios where base stations are difficult to deploy. With the help of deep reinforcement learning to train the intelligent body, it can formulate reasonable offloading decisions in a continuous and complex state space. It can also offload partial computing-intensive missions produced by users to edge servers for execution, thus improving the working and responding time of the system. However, at the moment, the fully connected neural networks used by the deep reinforcement learning algorithm are unable to handle the time-series data in the scenarios of UAV-assisted mobile edge computing (MEC). In addition, the training efficiency of the algorithm is low, and the decision-making performance is poor. To address the above problems, this study proposes a twin delayed deep deterministic policy gradient algorithm based on long short term memory (LSTM-TD3), using LSTM to improve the Actor-Critic network structure of the TD3 algorithm. In this way, the network is divided into three parts: the memory extraction unit containing LSTM, the current feature extraction unit, and the perceptual integration unit. Besides, the sample data in the experience pool are improved, and the historical data are defined, which provides the memory extraction unit with a better training effect. Simulation results show that, compared with the AC algorithm, the DQN algorithm, and the DDPG algorithm, the LSTM-TD3 algorithm has the best performance when optimizing the offloading strategy with the minimum total delay of the system as the target.