This paper studies satellite deorbit using electrodynamic tether (EDT) propulsion. Gaussian perturbation equations are used to model the orbital dynamics of EDT with environmental perturbations of electrodynamic force, aerodynamic drag and the effect of Earth’s oblateness. Differential equations for the induced voltage-current across EDT are derived and solved with boundary conditions determined by mission objectives and hardware devices. A simplified analytical method for solving the equations is proposed to improve computational efficiency. Simulations find that the orbit of a satellite deorbited by EDT will become elliptical in near polar orbits due to the higher-order perturbation of Earth’s magnetic field. This is beneficial for the near polar orbits where the electrodynamic force is less effective, because the atmosphere at a lower perigee will provide larger air drag to dissipate the orbital kinetic energy of satellite faster. Moreover, we proved that the polarity reverse of the induced voltage/current across EDT in near polar orbits does not affect the kinetic energy dissipation by the current induced Lorentz force. Compared the decay by air drag only, the orbit decaying time of a satellite with EDT will be reduced by three and two orders of magnitudes in the equatorial and polar orbits respectively.