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As a promising approach to assist the fifth-generation (5G) communication system, geostationary (GEO) satellite communication technology is expected to be utilized to provide an efficient and reliable coverage for the terrestrial cellular network. Most multi-beam GEO satellites work on the low-inclination GEO orbit. Due to various unexpected factors, e.g., the imperfect satellite orbit, attitude, and antenna deformation, the practical satellite beam pointing on the earth surface will deviate unfortunately from its designed theoretical location. Although the center boresight-to-ground point of the satellite multi-beam antenna can be maintained via the control of attitude bias and track retention, the practical beam pointing center would still experience inevitable deviations, causing unwanted ground coverage drifting in engineering applications. To combat this, in this paper, we first provide a comprehensive calculation approach for the actual beam pointing on the ground of a satellite multi-beam, which is also validated via the theoretical analysis on the measurement from a ground-based calibration station. On this basis, a simple yet effective data-driven model is established to characterize the dynamical deviating trends induced by various unexpected influences. Finally, a novel beam pointing calibration scheme is designed, based on the Kalman filter. By tracking the coupling coefficients between elevation angle and azimuth angle in our simple model, a pre-deformation is added to the designed beam. Our proposed approach for the beam pointing calibration is validated by the numerical simulations. An improvement of 78.26% is achieved in maximum ground-surface pointing deviation distance.