With the development of global satellite navigation systems, kinematic Precise Point Positioning (PPP) is facing the increasing computational load of instantaneous (single-epoch) processing due to more and more visible satellites. At this time, the satellite selection algorithm that can effectively reduce the computational complexity causes us to consider its application in GPS/BDS/GLONASS kinematic PPP. Considering the characteristics of different systems and satellite selection algorithms, we proposed a new satellite selection approach (NSS model) which includes three different satellite selection algorithms (maximum volume algorithm, fast-rotating partition satellite selection algorithm, and elevation partition satellite selection algorithm). Additionally, the inheritance of ambiguity was also proposed to solve the situation of constantly re-estimated integer ambiguity when the satellite selection algorithm is used in PPP. The results show that the NSS model had a centimeter-level positioning accuracy when the original PPP and optimal dilution of precision (DOP) algorithm solution were compared in kinematic PPP based on the data at five multi-GNSS Experiment (MGEX) stations. It can also reduce a huge amount of computation at the same time. Thus, the application of the NSS model is an effective method to reduce the computational complexity and guarantee the final positioning accuracy in GPS/BDS/GLONASS kinematic PPP.