Single-frequency Precise Point Positioning (PPP) using a Global Navigation Satellite System (GNSS) has been attracting increasing interest in recent years due to its low cost and large number of users. Currently, the single-frequency PPP technique is mainly implemented using GPS observations. In order to improve the positioning accuracy and reduce the convergence time, we propose the combined GPS/GLONASS Single-Frequency (GGSF) PPP approach. The approach is based on the GRoup And PHase Ionospheric Correction (GRAPHIC) to remove the ionospheric effect. The performance of the GGSF PPP was tested using both static and kinematic datasets as well as different types of precise satellite orbit and clock correction data, and compared with GPS-only and GLONASS-only PPP solutions. The results show that the GGSF PPP accuracy degrades by a few centimetres using rapid/ultra-rapid products compared with final products. For the static GGSF PPP, the position filter typically converges at 71, 33 and 59 minutes in the East, North and Up directions, respectively. The corresponding positioning accuracies are 0·057, 0·028 and 0·121 m in the East, North and Up directions. Both positioning accuracy and convergence time have been improved by approximately 30% in comparison to the results from GPS-only or GLONASS-only single-frequency PPP. A kinematic GGSF PPP test was conducted and the results illustrate even more significant benefits of increased accuracy and reliability of PPP solutions by integrating GPS and GLONASS signals.