Aiming at the problems that the quadratic polynomial model in satellite clock bias prediction is susceptible to noise interference and poor prediction accuracy, this study constructs a Multi-GNSS satellite clock bias prediction method based on Long Short-Term Memory neural network (LSTM) and analyzes the model accuracy of different satellite systems and different clock types based on different modeling schemes. To confirm the validity and feasibility of the model, the LSTM model, the quadratic polynomial (QP) model and the QP-LSTM model are built based on 12h and 24h data, and the clock bias of 1h, 3h, 6h and 12h are predicted, respectively. The comparative analysis results of the prediction accuracy of three models show that the LSTM model has the best accuracy for 24 hours of modeling and 1 hour of prediction. In the Multi-GNSS satellite clock bias LSTM prediction model, Galileo system has the highest accuracy, followed by the BDS and GPS systems, and the GLONASS system has the lowest accuracy, with accuracies of 0.069 ns, 0.018 ns, 0.133 ns and 0.242 ns respectively. The prediction accuracy of different atomic clocks differs, with hydrogen clocks outperforming rubidium clocks and cesium clocks. The accuracy of the LSTM model is 27% higher than that of the QP-LSTM model and 36% higher than that of the QP model.