When a vehicle-borne tracking and position device is used to track a Low Earth Orbit(LEO) satellite,the obtained prediction data of the satellite orbit by the traditional satellite tracking software usually show a lower prediction accuracy. Meanwhile, the target is missed easily because of the cloud or zenith blind zones during the target tracking. To improve the satellite orbit prediction, this paper presents a new method which uses the improved Laplace method to predict satellite orbits based on the measured data by the vehicle-borne tracking and position device. In consideration of the prediction errors come from the prediction model, measuring axis and the coordinate transfer, it proposes an interpolation method to correct the error between predicted value and actual measured value and to obtain a higher accuracy direction value. The testing data show the accuracy of predicted data has increased from 3′ to 10″ in azimuth and elevation when the data are extrapolated to 7 s, which realizes the stable satellite tracking in the cloud or zenith blind zones.