This paper investigated the nonholonomic motion planning of the underactrated spacecraft.The attitude motion of a rigid spacecraft can be controlled by using three momentum wheels.If one of the momentum wheels fails, the complete spacecraft equations are not controllable.If the total angular momentum of the system is zero,the control problem of the spacecraft attitude becomes a steering problem for a drift free control system.Based on the optimal control theory,a genetic algorithm for steering a rigid spacecraft with two momentum wheels was proposed,and the numerical simulation proved the genetic algorithm to be effective.