In general, spacecraft are designed to be maneuvered to achieve pointing objectives. To reorient the spacecraft with zero angular velocity at the end of the maneuver, a three-axis control design is usually used. When an actuator fails among three actuators, one must achieve these objectives using two control inputs, so that new control laws need to be considered. A simple and novel control law, which is based on the sequential Euler angle rotation strategy, is addressed. This paper explores a near minimum time control problem with constrained control input magnitudes. By introducing the three sequential sub-maneuvers with Euler-angle transformations, the governing nonlinear equations become rigorously linear, which permits a closed-form solution to be obtained for the switch times and final time, where the three sub-maneuvers are coupled through the unknown switch times. A numerical example demonstrates that the three-dimensional maneuver for an asymmetric spacecraft with two constrained control inputs can be successfully performed using the proposed closed-form solution. Published by Elsevier Ltd.