Laser trackers are instruments used to measure the three-dimensional coordinates of objects with high precision. It is necessary to study calibration methods to identify geometric errors of laser trackers so as to compensate for errors and improve measurement accuracy. Among the offsets, tilts, and eccentricity errors in the system, the transit tilt and offset errors play important roles and have an essential effect on the measurement accuracy, which need to be calibrated and compensated for. Current methods for detecting geometric errors between the transit and standing axes are complex and time-consuming. In this paper, a fast and novel calibration method is proposed, which can be easily operated with high precision. Two test rods are coaxially mounted on the ends of the transit axis to extend the hidden transit axis. Then, a telecentric measurement system is used to record the projection images of the test rods and identify the position of the transit axis. The transit offset and tilt errors were thus obtained by comparing the central axis positions of the two test rods before and after the standing axis rotated 180 degrees. Moreover, a numerical analysis method was proposed based on the least square circle fitting method to calibrate the installation eccentricity errors of the test rods. Experimental results verify that the measurement accuracy of the laser tracker can be improved after error compensation using the calibrated transit offset and tilt errors. The measurement error of the laser tracker can be reduced from 161 µm to about 73 µm after compensation at a distance of 5 m, while the error can be decreased from 143 µm to about 108 µm at a distance of 10 m.