The current registration method based on point features is susceptible to the quality of point clouds, involving large amounts of computation and having low efficiency. Meanwhile, the line feature methods have a single feature description and are limited to two-dimensional transformations, making it difficult to adapt to complex three-dimensional scenarios. This study proposes a point cloud registration method based on 3D linear multi-feature description and matching. Firstly, it uses the multi-scale curvature feature to extract key points of the point cloud and adopts a two-stage fitting method to obtain the key point lines. Then, it performs multi-feature expression based on angle and distance for the fitted lines, constructing a multi-feature descriptor and matching similar lines. Finally, the gradient descent method integrated with the random sample consensus (RANSAC) idea is used to calculate the optimal spatial transformation parameters between matching lines and the spatial transformation is carried out to complete the registration. Using the Stanford 3D point cloud database as experimental data and comparing the proposed method with existing registration methods, the results show that the registration accuracy of the proposed method can reach up to 10^-8 m. In addition, the registration efficiency and registration effect of this method in extreme positions are significantly better than those of other comparison methods.