Low Earth Orbit (LEO) Satellite Internet Network (LEO-SIN) is a promising approach to global Gigabit per second (Gbps) broadband communications in the coming sixth-generation (6G) era. This paper mainly focuses on the innovation of accuracy improvement of simulation modeling of the Doppler Power Spectrum (DPS) of satellite channels in LEO-SIN. Existing DPS modeling methods are based on Rice’s Sum-of-Sinusoids (SOS) which have obvious modeling errors in scenarios with main signal propagation paths, asymmetrical power spectrum, and random multi-path signals with a random Angle of Arrival (AOA) in LEO-SIN. There are few state-of-art researches devoted to higher accuracy of DPS modeling for simulation. Therefore, this paper proposes a novel Random Method of Exact Doppler Spread method Set Partitioning (RMEDS-SP). Distinct from existed researches, we firstly model the DPS of LEO-SIN, which more accurately describes the characteristics of frequency dispersion with the main path and multi-path signals with random AOA. Furthermore, piecewise functions to the Autocorrelation Function (ACF) of RMEDS-SP is first exploited to converge the modeling error supposition with time by periodic changes, which further improve the accuracy of the DPS model. Experimental results show that the accuracy of DPS in our proposed model is improved by 32.19% and 18.52%, respectively when compared with existing models.