The point clouds collected by Kinect have a large quantity and position errors, and it is inefficient to directly apply the Iterative Closest Point (ICP) algorithm to point cloud registration. To solve this problem, we propose an improved point cloud registration algorithm based on the angle between the normal vectors of feature points. First, the voxel grids are used to down sample the original point clouds collected by Kinect and reduce the number of point clouds and a filter is applied to remove the outliers. Then, the Scale Invariant Feature Transform (SIFT) algorithm is employed to extract the common feature points between the target point clouds and the point clouds to be registered, and the angle between the normal vectors of feature points is calculated to adjust the point cloud pose. Thus, the initial registration of the point clouds is completed. Finally, the ICP algorithm is applied to complete the fine registration of the point clouds. The experimental results show that compared with the traditional ICP algorithm, the proposed algorithm, while ensuring the registration accuracy, can improve the registration efficiency of point clouds and has high applicability and robustness.