In the environment of earth gravitation and magnetic field, the influence of aerodynamic drag was considered. The chaotic phenomenon was discussed when the magnetic rigid spacecraft without internal damping was on a circular orbit round the earth. The dynamical model was established by the law of moment of momentum. The Melnikov analysis was carried out to verify that the chaotic phenomenon is possible, and the numerical simulations were used to analysize the systematic dynamical motion. The theory analysis results agree with numerical simulations.