This paper proposes a planning method of the theoretically fastest slew path, and correspondingly, an analytical open-loop control law for the minimum-time eigenaxis rotation of spacecraft with three reaction wheels. The path planning and the control law are based on the angular momentum conservation of the spacecraft system. Then, a control scheme is also proposed to correct the maneuver error caused by model uncertainties. The control law and control scheme are verified in numerical simulation cases. The results show that the control law would realize the fastest slew path for an eigenaxis rotation, and the control scheme is feasible in shortening the slew time.