The invention relates to a satellite fast high-precision extrapolation method of a great-eccentricity track. A task track of a martian detector is an elliptic track with great eccentricity (e is greater than 0.6), a numerical integration method is adopted, and in order to realize the high-precision track calculation, the consideration of higher-order martian shape perturbation and the influence of other perturbation factors is needed, so the calculation quantity is greater, and the numerical integration method can be interrupted when a satellite computer resets or is switched; an analytical method is only applicable to the elliptic track with smaller eccentricity (e is smaller than 0.6); and the detector position provided by a precise track is utilized for fitting the Chebyshev multinomial coefficient, so greater fitting errors can be brought. The satellite fast high-precision extrapolation method has the advantages that the position difference of the precise track and the two-body track is introduced, the position difference is utilized for fitting the Chebyshev multinomial coefficient, the calculation problem of the satellite track of the elliptic track with great eccentricity can be perfectly solved, the calculation quantity is small, and in addition, the precision is high.