The BeiDou navigation satellite system (BDS-3) has been deployed and provides positioning, navigation, and timing (PNT) services for users all over the world. On the basis of BDS-2 system signals, BDS-3 adds B1C, B2a, B2b, and other signals to realize compatibility and interoperability with other global navigation satellite systems (GNSS). Network real-time kinematic (RTK) technology is an important real-time regional high-precision GNSS positioning technology. Combined with the network RTK high-precision service platform software developed by the author’s research group and the measured data of a provincial continuously operating reference station (CORS) in Hubei, this paper preliminarily evaluates the network RTK service performance under the new signal system of BDS-3. The results show that single BDS-3 adopts the new signal combination (B1C+B2a) and transition signal combination (B1I+B3I) when providing virtual reference station (VRS) services, the RTK fixation rate of the terminal is above 95%, and the horizontal and elevation accuracies are within 1cm and 2 cm, respectively, which meets the requirements of providing high-precision network RTK services by a single BDS-3 system. In addition, the positioning accuracy of BDS-2 is relatively poor, while the accuracy of BDS-3 is better than global positioning systems (GPS) and BDS-2. The combined processing effect of the B1I+B3I transition signal of BDS-2/3 is optimal, the accuracy of E and N directions is better than 0.5 cm, and the accuracy of U direction is better than 1.5 cm. It can be seen from the atmosphere correction accuracy, regional error modeling accuracy, and network RTK terminal positioning accuracy that the service effect of the B1C+B2a combination is slightly better than that of the B1I+B3I combination. When a single BDS-3 constellation provides network RTK services, it is recommended to use the B1C+B2a combination as the main frequency solution, and when the BDS-2/3 constellation provides service, it is recommended to use the B1I+B3I combination as the main frequency solution.