To overcome the speed limit of the traditional satellite orbit prediction method and lay foundation for independent orbital transfer planning of on-orbit satellites, the graphics processing unit (GPU) parallel computing method was utilized to accelerate the multi-satellite orbit calculation, and the parallel prediction module of orbit prediction was constructed, which realized the acceleration of satellite orbit prediction. In order to improve the calculation speed when the calculation amount is low, a monolithic GPU acceleration method was proposed, which substituted the simplified general perturbation version 4 (SGP4) calculation model into the kernel function. The computer memory only needed to interact with the GPU once, which greatly shortened the data transmission time between the memory and the GPU. Compared with the modular GPU acceleration method, the speed for medium or low scale calculations was increased greatly. The proposed monolithic acceleration method was implemented on two devices based on compute unified device architecture (CUDA) library. On NIVIDA TX2, a small embedded development board, it could realize the orbit prediction of 500 satellites for one day in 5 s (86 400 steps for each satellite), while the GPU acceleration ratio on the laptop was 4.6 times more than that of the central processing unit (CPU), and the precision loss after the acceleration was low. The experiment showed that the monolithic acceleration method was suitable for the parallel calculation of low and medium scale calculations (the number of steps is less than four million), and the modular acceleration method was suitable for the parallel calculation of large scale calculations (the number of steps is more than four million).