A kind of single-frequency precise point positioning (PPP) algorithm based on the raw observations is presented in this paper. By this algorithm, the ionospheric delays were corrected efficiently by means of adding the ionospheric delay prior information and the virtual observation equations with the spatial and temporal constraints, and they were estimated as the unknown parameters simultaneously with other positioning parameters. Then, a dataset of 178 International GNSS Service (IGS) stations at day 72 in 2012 was used to evaluate the convergence speed, the positioning accuracy and the accuracy of the retrieved ionospheric VTEC. The series of results have shown that the convergence speed and stability of the new algorithm are much better than the traditional PPP algorithm, and the positioning accuracy of about 2-3 cm and 2-3 dm can be achieved respectively for static and kinematic positioning with the single-frequency observations' daily solution. The average bias of ionospheric total electron content retrieved by the single-frequency PPP and dual-frequency PPP is less than 5 TECU. So the ionospheric total electron content can be used as a kind of auxiliary products in GPS positioning.