Based on the electron motion equation, the propagation of terahertz (THz) wave in plasma is studied. The complex refractive index of THz wave is determined by the plasma electron density and collisions. It decides the propagation of the THz in plasma, which means the change of the THz wave phase and amplitude. THz time-domain spectroscopy system can measure the THz wave phase and amplitude, so it can be used to diagnose the electron density and collisions. Limited by the dispersion relation in plasma, there is a limitation for this method in the electron density measurement. The diagnosis works well for plasmas with density in the range 1012~1016/cm3.