To improve the prediction accuracy of the primary frequency modulation capability of thermal power units and assist in ensuring grid frequency stability and safe operation of the power system, a primary frequency modulation capability prediction method is proposed that combines the Kepler Optimization Algorithm (KOA) with the Gated Recurrent Unit (GRU) network. Taking the actual operation data of primary frequency modulation of a 350 MW coal-fired thermal power unit as the sample, key characteristic variables were extracted through correlation analysis. The hyperparameters of GRU network model were optimized using KOA to construct a KOA-GRU prediction model, which was further compared with the Long Short-term Memory (LSTM) network model, the Particle Swarm Optimization (PSO) network model, the original GRU network model, and PSO-GRU network model. The results showed that the fitness value of the KOA-GRU network model stabilized at 0.127 after 7 iterations, indicating better convergence performance than the other four models. Meanwhile, the proposed model exhibited superior prediction performance under various evaluation metrics, with the Root Mean Square Error (RMSE) reaching 0.148 MW and the Mean Absolute Error (MAE) dropping to 0.092 MW, which demonstrated high prediction accuracy.