When obtaining the point cloud of an object to be measured by three-dimensional scanning, noise points and outliers will inevitably appear, which will significantly affect the accuracy of point cloud plane parameter estimation and plane fitting. An algorithm that combines random sampling consensus (RANSAC) and principal component analysis (PCA) can effectively estimate point cloud plane parameters and fit the plane, with some degree of robustness. However, the RANSAC algorithm needs to judge in each iteration process to distinguish between inner and outer points, which introduces redundancy and affects operation efficiency. Furthermore, its estimation results will be affected by the number of iterations. To solve the above problems, an algorithm that combines least square median (LMedS) and PCA is proposed to fit the point cloud plane, and three point cloud models are selected for experiments: Semantic3D outdoor scene point cloud database, part surface point cloud obtained using a line laser sensor, and indoor dataset of Princeton University. The experimental results show that, in the 100000 order of magnitude point cloud, the LMedS algorithm can effectively estimate the plane parameters of point clouds. Compared with the RANSAC algorithm, the LMedS algorithm can effectively estimate a plane model, with increased running speed, in less time, and with the same accuracy. The proposed method is a point cloud plane fitting method with strong robustness and advantages.