In this paper, a kinematic calibration method is proposed to improve the accuracy of a 7R 6-DOF robot with non-spherical wrist, where the parameters identifiability analysis and model reduction are particularly addressed in the identification procedure. Firstly, the kinematic error model of the robot is constructed based on the modified DH (MDH) model. Secondly, in order to derive a minimal model which is more suitable for practical application, model reduction is implemented considering compensability and constraints of the parameters defined in the controller, and QR decomposition is utilized to determine the redundant parameters, which are then removed in practical parameter identification. Finally, by using a laser tracker as the measuring device, a two-step procedure for error parameter estimation is proposed: (1) estimation of the robot base location with respect to the measurement coordinate system; (2) fine estimation of the identifiable kinematic parameters according to the measurement data. The experiment on a 7R 6-DOF industrial painting robot is implemented, the results show that the proposed method can effectively improve the accuracy of the robot.