An algorithm for point cloud registration in multidirectional affine transformation with variance compensation is proposed based on the statistical characteristics and shape features of point clouds, in which the problem for solving the unknown scaling factors is transformed into the problem for solving matrix eigenvalues by the overdetermined nonlinear equations, and the least square method is used for the unbiased estimation of noise variance by the quadric surface fitting. The similarity of the global vector features of point clouds is introduced, and the true value of the scaling factor is calculated by maximizing the similarity. The point cloud registration in multi-directional affine transformation is transformed into the rigid registration, and then the point cloud is registered with the main direction method. The simulation results show that the proposed algorithm has higher accuracy and smaller time consumption compared with the other existing registration algorithms when the point cloud is randomly lost or registered with noise.