Various methods for precise orbit determination (POD) of low earth orbiters (LEO) are briefly introduced in this paper. Based on the software named SHORD-III developed by our institute, single-difference (SD) and zero-difference (ZD) dynamic POD based on LEO carrying an on-board GPS receiver is mainly discussed. The approaches are tested using real GRACE data (November 5-25, 2002) and independently validated with Satellite Laser Ranging (SLR) measurements over the same 21 days. Comparisons with the scientific orbits provided by GFZ indicate that the SD POD RMS accuracy can achieve 5, 10 and 6 cm in radial, along and cross the track, and the ZD POD RMS accuracy can achieve 4, 8 and 4 cm in radial, along and cross the track. SLR validation shows that SD POD accuracy is better than 8 cm in distance, and ZD POD accuracy is better than 6 cm.