With the development of the GNSS and low earth orbit (LEO) satellites, the techniques of GNSS navigation and positioning are becoming increasingly important. In this contribuition, we investigate the Real-time kinematic (RTK)positioning performance for medium-to-long baselines based on the LEO constellation augmented GPS, where a LEO ranging satellite contributes to the geometric diversity by its fast-moving property. We define a new system by adding the LEO ranging satellite transmitting signals on the L1 and/or L2 band to the GPS ,and design three LEO constellations with different satellite numbers. The preliminary result of LEO augmented GPS RTK shows that the convergence time of about 45.04 km baseline can be shortened by 31.66%, 86.17% and 92.42%, respectively, with the augmentation of 54-, 162- and 324-satellite LEO constellation , and meanwhile , the augmentation capability is also found to be associated with length of baseline, the longer baseline , the better performance. For example, the convergence time of 162-satellite LEO constellation augmented GPS RTK can be shortened by 64.08%, 76.03% and 86.17%, respectively with 26.74 km, 34.50 km and 45.04 km baseline. Furthermore, the performance of time to first fix (TTFF) on LEO augmented GPS RTK is evaluated. The TTFF of 162-satellite LEO constellation scheme is shortened by 70~80% respectively with 20~50km baseline. And the TTFF of 26.74 km baseline is shortened by 35.92%,73.06% and 64.58%. The TTFF increases when the number of visible satellites increases,because ambiguity can not be fully fixed. In the next step, Partial ambiguity resolution will be applied on LEO augmented GPS RTK to improve the preliminary results above, as meanwhile, the performance of schemes with different intervals , station latitude, and the altitude of LEO satellite orbit will also be further analysed.