Day-ahead forecasting of solar radiation is essential for grid balancing, real-time unit dispatching, scheduling and trading in the solar energy utilization system. In order to provide reliable forecasts of solar radiation, a novel hybrid model is proposed in this study. The hybrid model consists of two modules: a mesoscale numerical weather prediction model (WRF: Weather Research and Forecasting) and Kalman filter. However, the Kalman filter is less likely to predict sudden changes in the forecasting errors. To address this shortcoming, we develop a new framework to implement a Kalman filter based on the clearness index. The performance of this hybrid model is evaluated using a one-year dataset of solar radiation taken from a photovoltaic plant located at Maizuru, Japan and Qinghai, China, respectively. The numerical results reveal that the proposed hybrid model performs much better in comparison with the WRF-alone forecasts under different sky conditions. In particular, in the case of clear sky conditions, the hybrid model can improve the forecasting accuracy by 95.7% and 90.9% in mean bias error (MBE), and 42.2% and 26.8% in root mean square error (RMSE) for Maizuru and Qinghai sites, respectively.