Abstract: In most radio-telescope pointing calibrations in China and abroad linear calibration models are used.The linear models do not consider the impact of nonlinear deviations on telescope pointing, and their calibration accuracies are rather limited.In this paper we present a new pointing-calibration method that includes correction for nonlinear deviations of the tilts of the azimuth axis of the antenna of a large-aperture radio telescope movable on a rail.We have applied the method to the Miyun 50m radio telescope of the NAOC.For the 50m radio telescope we measured roughness along its entire rail track and used the finite-element method to simulate nonlinear deviations of the tilts of the azimuth axis of its antenna.We also measured altitude errors of the antenna caused by rail-track roughness.The measurements are consistent with our finite-element simulations based on our new method and our measured rail-track roughness values, and thus verify the new method.We have carried out an experiment of pointing calibration of the 50m radio telescope using our new method.Compared to a conventional linear calibration model, our nonlinear model improves pointing accuracies by 0.5783 arcsecond on average.