Aiming at the problem of high difficulty and low precision of two point cloud registration with low overlap rate, a point cloud registration method combining clustering region partitioning with convex optimization problem is proposed. First, the curvature feature of point cloud is used to establish multi-scale descriptor to ensure the integrity of point cloud data and minimize redundant data. Second, the angle difference of multi-scale descriptor is used to cluster and block the corresponding relationship to obtain the overlap area of the source point cloud and the target point cloud. Finally, the point clouds in the overlap area and their corresponding relations are substituted into the convex optimization problem to remove outliers and optimize the corresponding relations to achieve the coarse registration, and then the iterative closest point algorithm is used to refine. Experimental results show that the proposed algorithm can narrow the useful search range of point cloud registration, reduce the amount of registration computation, and provide more advantageous registration accuracy and time efficiency for point cloud data with low initial overlap.