In multiple UAV systems, it is a challenging task to ensure accurate positioning of moving targets and stable trajectory prediction. Among them, the loss of moving target location is one of the main obstacles that affect the real-time and accuracy of multi-UAV system. To solve these challenges, this paper proposes a trajectory prediction algorithm combining Kalman filter and LSTM error compensation to solve the problem of location loss that may occur after multiple UAVs locate targets. The trajectory prediction is divided into two stages. Firstly, in the positioning stage, the Kalman filter prediction algorithm is used to obtain the algorithmic error. This error is then utilized for the error prediction LSTM network and the completion LSTM network. Secondly, in the positioning loss stage, the missing information is supplemented using the completion LSTM network. The trajectory for the target in the future period is obtained by combining the Kalman filter prediction with the error predicted by the error prediction LSTM network. Experimental results show that the proposed algorithm can effectively predict the target trajectory, and compared with the unimproved KF prediction algorithm, the RMSE of the proposed algorithm is reduced by about 4.46 times in straight prediction and 9.17 times in turn prediction.