The point cloud registration method that uses point features may fail owing to its inability to obtain corresponding points when the point cloud data collected by different stations has the occlusion problem. Therefore, a registration adjustment model is established in this study to iteratively calculate the translation vector and rotation matrix based on the equivalence of the plane normal vectors between the reference and unregistered stations; subsequently, the scale factor is evaluated based on the analytic geometry theory, and the medium errors with respect to the unit direction vector and moment vector deviations of the homonymous lines after registration are considered to be the indexes for evaluating the point cloud registration accuracy. The experimental results denote that the registration adjustment model can realize point cloud registration under the occlusion condition. Furthermore, the results denote that the medium errors of the moment vector deviations of the homonymous lines can be reduced to 0.0247 m after registration. This model not only retains the advantages of the dual quaternion regardless of the initial values of the parameters and the fast convergence rate, but also eliminates the restriction that the two endpoints of the lines need to be corresponding points.