Adding GLONASS data to GPS is a common way to enhance the performance of precise point positioning (PPP) in terms of convergence time and accuracy. However, the combined GPS/GLONASS PPP is not always guaranteed to provide a better solution than GPS PPP alone due to data quality issues. To improve this problem, we propose a new observation model for GPS/GLONASS PPP. We adopt a between-satellite single-difference (BSSD) combination and carrier smoothing (CS) techniques for GPS and GLONASS observations. The proposed BSSD-CS is shown to be effective in the improvement of performance of GPS/GLONASS PPP. A 7-day data set from 19 IGS stations are used to assess and verify the effectiveness of the proposed PPP model in static modes. Furthermore, three different GNSS receivers are used to investigate the potential of the proposed PPP model. It is shown that the proposed GPS/GLONASS PPP model can indeed reduce the convergence time and achieve better positioning precision in comparison with traditional GPS/GLONASS PPP models. In addition, even used with a low-cost GNSS receiver, the proposed PPP can still yield decimeter-level positioning accuracy and precision within a few minutes, which is as precise as and as fast as using a high-end GNSS receiver.