At present, there is a phenomenon of network data packet loss in the trajectory tracking control system, which will degrade or even destabilize the system’s performance. Therefore, this work first explains the theory of the deep long-short term memory (LSTM) neural network model, the kinematic model of mobile robots, and the trajectory tracking error model. The reasons for data packet loss in the control system are analyzed. Second, a prediction model based on the LSTM network is designed according to the theory mentioned above. Finally, the training effect of the LSTM model and the robot trajectory tracking effect based on the model are tested by setting up simulation experiments. The research results are as follows: (1) The pose test error of the mobile robot will eventually tend to zero through the simulation curve generated by the pose parameters (x, y, θ) of the mobile robot. (2) The trajectory tracking error of the deep LSTM neural network prediction and compensation method with the packet loss rate of 5% is less than that with the packet loss rate of 10%. (3) The linear velocity
υ
of the mobile robot based on the prediction model of the LSTM network varies greatly but is always in the interval (−2, 2). Its angular velocity
ω
initially fluctuates greatly but gradually tends to zero after about 13 s. (4) When the prediction model tracks the trajectory of the robot, the horizontal position x, the vertical position y, and the angle
θ
coincide with the reference trajectory. The exploration is conducted to provide a reference for the research on data packet loss in the networked mobile robot trajectory tracking system.