By August 2016, 5 new-generation BeiDou satellites (BeiDou-3) have successfully been launched. The observations of a very limited number of 9 International GNSS (Global Navigation Satellite System) Monitoring and Assessment Service (iGMAS) stations and 52 Multi-GNSS Experiment (MGEX) stations from 16 July to 14 August 2016 are processed to determine the orbits of BeiDou-3 and BeiDou-2 satellites, respectively. The internal consistency and satellite laser ranging (SLR) validations are conducted for the orbit validation. BeiDou-3 MEO (Medium Earth Orbit) (C33 and C34) have larger root mean square (RMS) values than those BeiDou-3 IGSO (C31 and C32), whereas BeiDou-2 MEO satellites have smaller RMS values than the BeiDou-2 IGSO satellites. Furthermore, BeiDou-3 IGSO and BeiDou-2 satellites have RMS values at identical levels, whereas BeiDou-3 MEO satellites have larger RMS values than the BeiDou-2 MEO satellites. The RMS residuals are approximately 10 cm in the radial component and approximately 25 cm in the along component for BeiDou-3 IGSO satellites. For BeiDou-3 MEO satellites, the RMS residuals are approximately 40 cm in the radial component and approximately 60 cm in the along component. The SLR validation reports that the orbit radial component can reach an accuracy on the level of 1 decimeter and 4 decimeters for BeiDou-3 IGSO and MEO, respectively.