To improve the interception ability of the defensive missile in three-body game scenarios, predicting the trajectory of the incoming target is essential. However, due to the limited transfer rate of the data link, the update frequency of the target information is low, which leads to the traditional prediction method based on Kalman filter and trajectory fitting being no longer applicable. Therefore, this paper proposed a trajectory prediction method based on backpropagation neural network and least squares method (TPM-BPNN-LSM) under low-information support conditions. Initially, the trajectory library of the incoming target is created based on the detectability of the airborne radar. Next, the nonlinear relationship hidden in the trajectory library is learned by BP neural network. In online prediction, the optimal initial-states estimation of the incoming target is solved by the least squares method according to the target information transmitted by data link, and then the trajectory prediction is realized. Simulation results demonstrate the high accuracy of TPM-BPNN-LSM under low information support condition.