The Low Earth Orbit (LEO) enhanced Global Navigation Satellite System (LeGNSS) relies on LEO satellites to broadcast GNSS-like navigation signals, providing real-time satellite orbit and clock information to enhance GNSS service performance. To ensure real-time positioning service, a period of orbit prediction becomes necessary due to the limited signal bandwidth and computation time delay. In contrast to traditional dynamic model, on-board accelerometers offer more accurate non-gravitational acceleration for LEO satellites. In this study, we improve the accuracy of short-term (1 hour) LEO satellite orbit prediction by utilizing predicted accelerometer data instead of the traditional dynamic model. We combine the Least Squares (LS) and Autoregressive (AR) methods to model and predict accelerometer data from the GRACE-A (500 km) and SWARM-A (460 km) satellites. In the experiment, the 1-hour prediction accuracy of the accelerometer data in the 3-Dimensional (3D) direction is 40.2 nm/s 2 for the GRACE-A satellite and 21.7 nm/s 2 for the SWARM-A satellite, respectively. When utilizing the predicted accelerometer data for 1-hour orbit predictions, the predicted orbit precision in the 3D direction is 0.21 m for the GRACE-A satellite and 0.15 m for the SWARM-A satellite, respectively. The orbit prediction accuracy shows an improvement of approximately 70% compared to the traditional dynamic model.