In distributed IoT application scenarios such as environmental monitoring, nodes often have different priorities due to the different regional importance of node monitoring and the amount of data collected. The dynamic change of node priority will make the UAV frequently replace the target node of data acquisition, resulting in prolonged task completion time and unwarranted waste of energy. Therefore, we propose a joint optimization algorithm of UAV task completion time and energy consumption based on DDQN for distributed IoT application scenarios with dynamic priority of nodes. During the training process, the UAV learns the optimal strategy under the constraints of task completion time, energy consumption and avoiding node data overflow. The simulation results show that compared with the maximum priority strategy and greedy strategy, the task completion time of the proposed algorithm is reduced by 9.2% and 15.1% respectively, and the energy consumption is reduced by 10% and 16.3% respectively. Compared with the DQN method, the proposed algorithm converges faster and the training process is more stable.