Irregularities in the Earth’s ionosphere can make the amplitude and phase of radio signals fluctuate rapidly, which is known as ionospheric scintillation. Severe ionospheric scintillation could affect the performance of the Global Navigation Satellite System (GNSS). Currently, the Multiple Phase Screen (MPS) technique is widely used in solving problems caused by weak and strong scintillations. Considering that Southern China is mainly located in the area where moderate and intense scintillation occur frequently, this paper built a model based on the MPS technique and discussed the scintillation impacts on China’s BeiDou navigation system. By using the BeiDou B1I signal, this paper analyzed the scintillation effects on the receiver, which includes the acquisition and tracking process. For acquisition process, this paper focused on the correlation peak and acquisition probability. For the tracking process, this paper focused on the carrier tracking loop and the code tracking loop. Simulation results show that under high scintillation intensity, the phase fluctuation could be −1.13 ± 0.087 rad to 1.40 ± 0.087 rad and the relative amplitude fluctuation could be −10 dB to 8 dB. As the scintillation intensity increased, the average correlation peak would decrease more than 8%, which could thus degrade acquisition performance. On the other hand, when the signal-to-noise ratio (SNR) is comparatively lower, the influence of strong scintillation on the phase locked loop (PLL) is much higher than that of weak scintillation. As the scintillation becomes more intense, PLL variance could consequently results in an error of more than 2.02 cm in carrier-phase based ranging. In addition, the delay locked loop (DLL) simulation results indicated that the pseudo-range error caused by strong scintillation could be more than 4 m and the consequent impact on positioning accuracy could be more than 6 m.