This paper combines deep reinforcement learning (DRL) with meta-learning and proposes a novel approach, named meta twin delayed deep deterministic policy gradient (Meta-TD3), to realize the control of unmanned aerial vehicle (UAV), allowing a UAV to quickly track a target in an environment where the motion of a target is uncertain. This approach can be applied to a variety of scenarios, such as wildlife protection, emergency aid, and remote sensing. We consider a multi-task experience replay buffer to provide data for the multi-task learning of the DRL algorithm, and we combine meta-learning to develop a multi-task reinforcement learning update method to ensure the generalization capability of reinforcement learning. Compared with the state-of-the-art algorithms, namely the deep deterministic policy gradient (DDPG) and twin delayed deep deterministic policy gradient (TD3), experimental results show that the Meta-TD3 algorithm has achieved a great improvement in terms of both convergence value and convergence rate. In a UAV target tracking problem, Meta-TD3 only requires a few steps to train to enable a UAV to adapt quickly to a new target movement mode more and maintain a better tracking effectiveness.