This paper presents a GNSS multi-frequency carrier tracking algorithm with a high-resolution cycle-slip detection and correction to address the loss-of-lock and cycle-slip issues during strong ionospheric scintillations. In the multi-frequency tracking design, a virtual fundamental carrier with longer wavelength was firstly constructed to associate multi-carriers according to the frequency diversity and dependency. The multi-carrier measurements are combined to perform inter-frequency aiding on the Doppler and Doppler rate estimations for each frequency channel, while each carrier phase will be tracked independently with consideration of phase divergence. Based on the realistic carrier phase estimation and fundamental geometric Doppler component, the geometry-free carrier phase can be obtained and used for high rate/high-resolution cycle-slip detection and correction in the signal tracking level. We use the simulated raw data to verify the proposed algorithm. The results confirm that the accuracy and robustness of the multi-frequency tracking can be guaranteed during the strong ionosphere scintillation. In addition, the small scale and fast cycle slips on each carrier can also be detected and repaired.