In order to improve the accuracy of the 2RPU/UPR+RP over-constrained hybrid robot in practical application and meet the requirements of production practice, the error compensation research of the robot was carried out. Firstly, the motion principle of the over-constrained hybrid robot was introduced. Then, the geometric error sources that affect the end precision of the hybrid robot were analyzed, and the zero calibration and full calibration method for improving the accuracy of the hybrid robot were introduced. The hybrid robot was divided into the parallel mechanism and the swing head with single-degree-of-freedom. Theoretical research on zero calibration and full calibration were conducted on these two parts respectively. Then the calibration experiment system was built up based on the laser tracker, and true values of error parameters were obtained by using algorithm after calibration, which were compensated to the kinematics algorithm. The result, indicates that the proposed full calibration and zero calibration method can effectively improve the positioning accuracy of the hybrid robot.