The space–air–ground information network (SAGIN) has been widely used due to its excellent performances including wide coverage and high flexibility. However, the dynamic network topology of SAGIN presents challenges for traditional protocols. The statistical priority-based multiple access (SPMA) control protocol has received widespread attention because it effectively allocates resources in networks with heterogeneous terminals and dynamic topology. However, the existing SPMA protocols suffer from issues like large errors and low prediction accuracy in channel load statistics. Therefore, this paper proposes an improved SPMA based on the bi-directional long short-term memory (BiLSTM) neural network. First, we analyze and correct errors in channel load statistics at the physical layer, then develop a BiLSTM-based channel load prediction model, and finally simulated the improved SPMA using Matlab. Experimental results show that the proposed channel load prediction model achieves good prediction accuracy, and the improved SPMA protocol markedly improves channel utilization, providing differentiated services for multi-priority businesses.