Abstract: Traveling ionospheric disturbance (TID) is a common observed ionospheric disturbance, which have impacts on the propagation process of electromagnetic wave at gigahertz (such as satellite navigation) signals. In order to investigate the propagation effect of TID on satellite navigation signal, this paper simulates the propagation of navigation signal in magnetized ionospheric plasmas based on three-dimensional ray tracing method. We focus on the second-order ionospheric effect and Doppler effect during ionospheric TID disturbance. Firstly, this paper establishes the TID generation model by adding disturbance into the NeQuick ionospheric model, which can simulate different scales of the TID structure. Secondly, the propagation characteristics of navigation signal in TID are obtained based on two virtual stations in the North and South of China. Then, the second-order ionospheric effect and Doppler parameters of navigation signals at different elevation and azimuth angles have been calculated. Finally, the TID parameters on the ionospheric second-order and Doppler effect have been analyzed. The simulation results show that the ionospheric second-order effect and Doppler effect may become more important for low elevation rays. Also, the Doppler effect is significantly correlated with the period of TID.