The E × B drift instability is studied in Hall thruster using one-dimensional particle in cell (PIC) simulation method. By using the dispersion relation, it is found that unstable modes occur only in discrete bands in k space at cyclotron harmonics. The results indicate that the number of unstable modes increases by increasing the exteal electric field and decreases by increasing the radial magnetic field. The ion mass does not affect the instability wavelength. Furthermore, the results confirm that there is an instability with short wavelength and high frequency. Finally, it is shown that the electron and ion distribution functions deviate from the initial state and eventually the instability is saturated by ion trapping in the azimuthal direction. Also for light mass ion, the frequency and phase velocity are very high that could lead to high electron mobility in the axial direction.