Abstract: Aiming at the problems of poor control effect of traditional PID control on reheat steam temperature and low precision and large error of traditional grey prediction model, firstly, the structure of traditional multi-variable grey prediction model GM（1,2） is improved to form a new multi-variable grey prediction model OGM（1,2）; and then, the sparrow search algorithm was used to optimize the generation coefficient of OGM（1,2） to find the generation coefficient value that minimized the average relative simulation percentage error of the intrinsic sequence; finally, combined with the traditional PID, the gray predictive control system is formed to control the reheat steam temperature. The simulation results show that compared with the traditional PID control, the control performance of the system is obviously improved, and the system has good robustness.