Cutback control in a grid code is one of the functions of a wind power plant (WPP) that is required to support the system protection and frequency stability. When a cutback control command signal is delivered to the WPP from the system operator, the output of a WPP should be decreased to 20% of the rated power within 5 s. In this paper, we propose a dedicated cutback control algorithm of a WPP based on the ratio of the command power to the available power. If a cutback control signal is delivered, the algorithm determines the pitch angle for the cutback control and starts the pitch angle control. The proposed algorithm keeps the rotor speed at the speed before the start of the cutback control to quickly recover the previous output prior to the cutback control. The performance of the algorithm was validated for a 100 MW aggregated WPP based on a permanent magnet synchronous generator under various wind conditions using an EMTP-RV simulator. The results clearly shows that the proposed algorithm not only successfully reduces the output to the command power within 5 s by minimizing the fluctuation of the pitch angle, but also rapidly recovers to the output level before the cutback control.