The BeiDou navigation satellite system with global coverage (BDS-3) has been fully operational since July 2020 and provides comprehensive services to global users. BDS-3 transmits several new navigational signals based on the signals inherited from the BeiDou navigation satellite (regional) system (BDS-2). Previous studies focused on the positioning performance of BDS-2 plus BDS-3 and that of combining BDS-3 and other Global Navigation Satellite Systems (GNSSs), but there was no in-depth discussion on the positioning performance of BDS-3 only. In this contribution, BDS-3-only Real-Time Kinematic (RTK) positioning is analysed using data collected in zero and short baselines in Wuhan, China. The RTK model based on single-differenced observations is first presented, and BDS-3-only RTK positioning in single- and dual-frequency cases is evaluated in terms of empirical integer ambiguity resolution success rates and positioning accuracy. The numerical tests suggest that the positioning performance for B1I, B3I and the new frequency B1C is comparable, while that for the new frequency B2a is poorer; the new frequency combination B1C+B2a is not as good as B1C only, owing to the unrealistic stochastic model used.