Robot accuracy calibration is an effective method to improve its kinematic accuracy. However, most of the existing calibration methods need to measure the complete set of 6-dimensional pose errors of the end-effector, which makes the calibration process especially complicated. In this paper, an accuracy calibration method for a 3-CRU translational parallel robot is proposed based on the subset of error measurements. The process is implemented by four steps: 1) the error model is established based on matrix method. Then the structural errors to be identified are separated. 2) part of pose errors of the end-effector are measured by laser tracker and used to form the subset of error measurements. 3) the minimum structural error linear combination affecting robot accuracy is determined according to the minimum parameter error linear combination theorem. After that, the structural errors can be identified based on the subset of error measurements. 4) error compensation based on the identification results. This method can not only ensure the identifiability of the structural errors, but also can realize error identification based on the subset of error measurements, which will significantly reduce the calibration workload and improve the calibration efficiency. Experiments are carried out to prove the effectiveness of the calibration method.