The update of the Android system and the emergence of the dual-frequency GNSS chips enable smartphones to acquire dual-frequency GNSS observations. In this paper, the GPS L1/L5 and Galileo E1/E5a dual-frequency PPP (precise point positioning) algorithm based on RTKLIB and GAMP was applied to analyze the positioning performance of the Xiaomi Mi 8 dual-frequency smartphone in static and kinematic modes. The results showed that in the static mode, the RMS position errors of the dual-frequency smartphone PPP solutions in the E, N, and U directions were 21.8 cm, 4.1 cm, and 11.0 cm, respectively, after convergence to 1 m within 102 min. The PPP of dual-frequency smartphone showed similar accuracy with geodetic receiver in single-frequency mode, while geodetic receiver in dual-frequency mode has higher accuracy. In the kinematic mode, the positioning track of the smartphone dual-frequency data had severe fluctuations, the positioning tracks derived from the smartphone and the geodetic receiver showed approximately difference of 3–5 m.