During the strong ionospheric scintillation, global positioning system (GPS) signal will be frequently subjected to amplitude fading, phase errors, increased carrier Doppler frequency shift, and even loss of lock. Based on GPS L1 C/A signals during the last peak of the solar cycle at the low latitude site of Sao José dos Campos, Brazil (23.2S, 45.9W) from 2013 to 2015, the relationship between amplitude/phase scintillation and carrier frequency is analyzed, and probability distribution function (PDF) model is proposed to achieve corresponding relationship quantified. According to certain threshold of peak probability boundary, the proportional trends of carrier frequency widths on four levels of scintillation are presented. Detailed analysis implies that different levels of scintillation will influence the fluctuation of carrier frequency, which will provide useful guidance to set the receiver’s bandwidth with respect to the different scintillation levels and design the advanced tracking algorithm.