The vision-guided robotic machining accuracy highly depends on the hand-eye calibration accuracy between robot and vision equipment. In order to address the problem of less parameter constraints in existing hand-eye calibration methods, in this paper a hand-eye calibration algorithm of binocular stereo vision is proposed based on multi-pixel 3D geometric centroid relocalization. The algorithm mainly includes three steps: 1) the checkerboard relocalization images of multiple sets of fixed-point pose transformations are captured by the binocular stereo vision; 2) the robot tool center point (TCP) coordinates in the binocular coordinate system are obtained by an iterative reweighted least squares algorithm based on sub-pixel corner extraction, and 3) the hand-eye transformation matrix between the binocular system and the robot is obtained by the singular value decomposition (SVD). The experimental results show that both the average error and the mean square error of the proposed hand-eye calibration algorithm can reach 0.45mm and 0.21mm, respectively, which are much smaller than the existing algorithms and can meet the accuracy requirements of robotic positioning and machining.