Generally speaking, the Euler angle is usually used to describe the attitude of small satellites. In this case, however, singularity exists during large angle maneuver of small satellites. In contrast, such singularity can be avoided when the attitude is described by the quaternion. In this article, with regard to nonlinear properties of small satellite attitude contol systems actuated by reaction wheels, the attitude kinematics is described by the error-quaternion so that the large angle maneuver of the satellite can be converted into the problem of regulation of the error-quaternion. Sliding surfaces were designed on the basis of error-quaternion and an equivalent variable-structure controller introducing angular velocity acceleration feedback term was derived based on Lyapunov theorem. Simulation results show that the the proposed SMC law can improve the convergence rate, reduce the overshoot value of angular volecity during the maneuver and the demand of initial control torquer. In the meanwhile global stability and robustness of the method considering parameter uncerties and external disturbances such as sunlight pressure moment, the surplus magnetism moment of satellite and the pneumatic moment can also be guaranteed.