We introduce a new model named the regional spherical harmonic model aimed at enhancing the pointing accuracy of alt-azimuth telescopes. Considering that the pointing accuracy of telescopes is influenced by a combination of mechanical and environmental errors, a mathematical model combining spherical harmonics and Fourier series is proposed to address the issue of data discontinuities observed during the observation process. In addition, a regional modeling approach was incorporated to further refine the accuracy. The model was validated using multi-day actual observation data from the Changchun 1-m diameter Cassegrain telescope with an alt-azimuth mounting (Changchun 1-m Telescope). Compared with classical pointing models, the proposed method significantly improves the pointing accuracy after calibration. The azimuth pointing accuracy reached 1.899 arcseconds, and the elevation pointing accuracy reached 0.913 arcseconds.