Precise Orbit Determination (POD) of the Inclined Geo-Synchronous Orbit (IGSO) satellite with onboard Global Navigation Satellite System (GNSS) measurements can achieve high precision, which can replace the technique using ground-based measurements. The LT4A, an IGSO satellite located at 89 degrees E with an orbital inclination of 16 degrees, is equipped with a high-sensitivity receiver designed to capture BDS B1I and GPS L1 signals. This study first evaluated data availability and measurement quality before analyzing the orbit accuracy of POD over 30-h and 72-h arcs. The results show that the LT4A onboard receiver can receive an average of 3.9 GPS satellites and 4.0 BDS satellites per epoch, with more than four satellites in 32.6 % of GPS epochs, 37.6 % of BDS epochs, and 98.5 % of combined GPS + BDS epochs. The position dilution of precision of GPS observations, BDS observations, and combined GPS + BDS observations are 21.7, 26.0, and 15.8, respectively. The cycle slip ratios of the GPS and BDS observations are 6.3 % and 28.9 %, respectively. From the data analysis, eliminating data with carrier-to-noise ratio less than 40 dB-Hz and signal height less than 2000 km is better for POD results. When using only GPS observations, only BDS observations, and combined GPS + BDS observations to determine the orbit, the Root Mean Square (RMS) of the pseudo-range residuals are about 3.1 m, 2.5 m, and 3.1 m, respectively, with corresponding carrier phase residuals of 9.5 cm, 4.4 cm, and 10.4 cm. The average RMS for 30-h POD arc overlaps are 4.091 m, 4.319 m, and 2.274 m, respectively, while laser ranging verification results are 0.994 m, 0.978 m, and 0.277 m, respectively. For the 72-h POD arc, the average orbit overlap RMS is 3.242 m, 3.199 m, and 1.807 m, respectively, with laser ranging verification results of 0.527 m, 0.687 m, and 0.356 m. Reprocessing onboard single point positioning data with dynamic models significantly reduces orbit error from about 106.2 m to 4.9 m.