In chest and abdomen robotic radiosurgery, due to the motion delay of the robotic manipulator, the tumor position tracking process has a period of delay. This delay ultimately affects the accuracy of radiosurgery treatment. To address the influence of the delay in robotic radiosurgery, a Long-and-Short-Term Memory (LSTM) network as a deep Recurrent Neural Network (RNN) has been applied in a prediction network model for respiratory motion tracking in recent years. However, patients' respiratory state may change in the process of treatment, which may influence the accuracy of prediction. Therefore, it is necessary to update the prediction network through additional data, such as the actual position of the tumor obtained by X-ray imaging. However, the LSTM network has a long update time, and it may not be able to complete the prediction model update in a cycle of X-ray acquisition. To solve this problem, a fast prediction model based on Bidirectional Gated Recurrent Unit (Bi-GRU), is proposed in this paper. This method can reduce the average updating time of the network model by 30%.