This paper proposes a new antiwindup strategy for PI speed controller to suppress the undesired side effect known as integrator windup when large set-point changes are made. When the speed control mode is changed from P control to PI control, an appropriate initial value for the integrator is assigned. This value then restricts the overshoot. In addition, the proposed method guarantees the designed performance independent of the operating conditions, i.e., different set-point changes and load torques, and can be easily implemented with existing PI controllers. In SIMULINK/MATLAB-based comparative simulations and experiments for a permanent-magnet synchronous motor speed controller, the proposed method shows a superior control performance compared with the existing well-known antiwindup methods, such as conditional integration and tracking back calculation.