To address the issue that existing radar-based precipitation extrapolation techniques can not adequately characterize the evolution of thunderstorms and cause systematic biases in heavy precipitation forecasts, this paper proposes a heavy precipitation extrapolation and correction method which integrates the evolution features of thunderstorms. Based on the storm cell identification and tracking (SCIT) algorithm, a thunderstorm development trend discrimination model is constructed for different thunderstorms by combining key factors including strong gradient zones, newly generated cells, and echo area changes. By utilizing radar reflectivity factor, optical flow vectors and dynamic Z-I relationship, we implement evolutionary constraints and corrections during the extrapolating process of heavy precipitation. Verification on the precipitation forecasts in the main flood season of 2025 shows that in the 0-1 h forecasts, the TS scores of the corrected products at the level of ≥20 mm·h-1 and ≥50 mm·h-1 are both higher than those of the optical flow system, with the advantage increasing with precipitation intensity. In the 1-2 h forecasts, the TS scores at ≥20 mm·h-1 and ≥50 mm·h-1 are still significantly improved compared with those of the optical system, but the score at ≥50 mm·h-1 is only 0.004, indicating very limited operational guidance value. Further analysis of typical cases of heavy precipitation demonstrates that the correction technique can capture precipitation characteristics of convective systems rapidly moving and developing to a greater extent and effectively alleviate the problems of underestimating intensity and coverage that exist inherently in traditional extrapolation methods.