A fast global registration algorithm for 3D point cloud is proposed, which is used to estimate the rigid pose relationship of any two sets of similar point clouds in space. First, the three principal component vectors of two groups of point clouds are calculated to form their own principal component (PC) coordinate systems with their respective center points. Then, in order to obtain the approximate pose relationship between the two similar groups of point clouds, the coordinate transformations of the two groups of point clouds are respectively performed, and the directions corresponding to the PC coordinate axes are corrected by the mean of Euclidean distances of some close points. After the above coarse registration, the two groups of point clouds can be matched fast and accurately at arbitrary position by the fast iterative closest point (ICP) algorithm. The experimental results show that the proposed method can achieve global registration for any two sets of point clouds with similar shape and completeness at any position in any pose, and has higher speed and accuracy.