As the angle measurement accuracy for a laser tracker affects the instrument measurement accuracy directly, a discrete calibration method for the angle measurement errors of a metal circular grating in the laser tracker was proposed based on an autocollimator combined with a multi-mirror polyhedron. The error compensation method based on harmonic analysis was studied. Then, a compensation model was built up on the basis of the harmonic wave components whose amplitudes are large and phases remain essentially constant, by which the no convergence from least square method was overcome. Futhermore, the calibration uncertainty of angle measurement errors was analyzed. The analysis results show that the horizontal angle measurement accuracy is reduced from 1.60″ to 0.90″, and the vertical angle from 4.89″ to 0.91″ after compensation. The accuracy is improved by 44% and 81% respectively, and has been from an arc second scale to a sub-arc second scale. The results indicate that the proposed method effectively compensates angle measurement errors for harmonic and vertical axis systems of the laser tracker, and also provides a reference for other error compensation of angle measuring systems.