The Earth's ionosphere can hinder radio propagation with two serious problems: group delay and phase advance. Ionospheric irregularities are significantly troublesome since they make the amplitude and phase of the radio signals fluctuate rapidly, which is known as ionospheric scintillation. Severe ionospheric scintillation could cause loss of phase lock, which would degrade the positioning accuracy and affect the performance of navigation systems. Based on the phase screen model, this paper presents a novel power spectrum model of phase scintillation and a model of amplitude scintillation. Preliminary results show that, when scintillation intensity increases, the random phase and amplitude fluctuations become stronger, coinciding with the observations. Simulations of the scintillation effects on the acquisition of Beidou signals predict acquisition probability. In addition, acquisition probabilities of GPS and Beidou signals under different scintillation intensities are presented. And by the same SNR the acquisition probability decreases when the scintillation intensity increases. The simulation result shows that scintillation could cause the loss of the acquisition performance of Beidou navigation system. According to the comparison of Beidou and GPS simulations, the code length and code rate of satellite signals have an effect on the acquisition performance of navigation system.