Since November 2017, eight BeiDou global navigation system (BDS-3) satellites equipped with Ka-band inter-satellite link (ISL) payloads have been launched into medium earth orbit. We present the precise orbit determination (POD) for BDS-3 satellites using both L-band satellite-ground and Ka-band ISL observations. The satellite-ground tracking data are collected from the international GNSS Monitoring and Assessment System stations. The data period is DOY (day of year) 127–156, 2018. The BDS-3 ISL measurements are described by a dual one-way observation model. After transforming the dual one-way observations to the same epoch, clock-free and geometry-free observables can be obtained by the addition and subtraction of dual one-way observations. Using the geometry-free observables, the ISL measurement noise is analyzed and confirmed to be less than 10 cm. Using the clock-free observables and ground tracking data, the precise orbits are determined together with combined ISL hardware delays. For the estimates of hardware delays, the mean STD is 0.08 ns. For the satellite orbits, the ground-only POD solutions are also computed for comparison. When using 16 globally distributed ground stations, the addition of the ISLs improves the POD performance. For example, the 3D RMS of orbit overlap differences is reduced from 15.9 cm to 9.2 cm, yielding an improvement of 42% compared to ground-only POD. When only 6 stations in China are used for POD, the addition of ISLs enables the 3D RMS to be reduced from 85.4 cm to 14.8 cm with a greater improvement of 83%.