The three-axis attitude control of magnetic actuated rigid spacecraft is considered in this paper. In the presented work, second order sliding mode control (2-SMC) with a nonlinear sliding surface is considered to generate continuous control with a finite time convergence property. The super-twisting control algorithm is considered for 2-SMC. The simulation results show that super-twisting based control with considered nonlinear sliding surface, is able to generate sufficient control torque, which results three-axis controllable spacecraft. Results show that controller steers the attitude trajectories to their nearest equilibrium. The robustness of controller is evaluated by subjecting cyclic disturbance torques, and inertia uncertainty.