The classic iterative closest point algorithm is sensitive to the initial position and may fall into a local optimal solution. However, if coarse registration is carried out first to adjust the position and pose, it will take a long time to calculate. Thus, an efficient point cloud registration algorithm based on principal component analysis (PCA) is proposed. First, PCA was used to identify the principal axis directions between the two point clouds. Subsequently, the coordinate system was transformed based on the relationship between two principal axes. Finally, the distance between the contour points on the axes was used for correction to avoid spindle reverse. Compared with the typical error correction method, this approach greatly reduces calculation time. The experimental results show that the improved PCA registration algorithm reduces the running time by 80% on average, and the computational efficiency is significantly improved for point clouds containing more than 20000 points. Further, the algorithm addresses poor initial position and realizes the rapid registration of the two point clouds under any pose. Moreover, the algorithm can be applied to the 3D point cloud registration of train components to improve registration efficiency.