Abstract: The accuracy of low earth orbit (LEO) satellite orbits directly affects the application areas of LEO satellites, so it’s very meaningful and necessary work so as to study appropriate models to improve the fitting/forecasting accuracy of LEO satellite orbit. The fitting/forecasting accuracy of sliding Chebyshev polynomial and Kriging algorithm in different types of LEO orbits were studied in this paper, the results show that: both algorithms can obtain millimeter-level interpolation accuracy with a suitable fitting strategy. Compared to the sliding Chebyshev fitting algorithm, the spatial error distribution of the kriging algorithm fitting orbit is more concentrated, and it does not fluctuate sharply with the change of epoch. The prediction accuracy of the Kriging algorithm is lower than the sliding Chebyshev polynomial. When the Kriging algorithm is used to forecast 60 seconds, the forecasting accuracy can reach 1 to 2.5 m. While the sliding Chebyshev polynomial’s forecasting accuracy of 120 seconds is better than 5 m in each LEO satellite.