A point cloud alignment algorithm based on statistical local feature description and matching is proposed to address the problems of poor robustness and low alignment accuracy of the ICP algorithm in the presence of poor initial positional, partial data loss, and noise interference. Firstly, a 4-dimensional statistical local feature descriptor is constructed using point cloud local density, point cloud fitting plane distance variance, Gaussian curvature, and mean curvature to accurately describe the local features of the query points. Then, the corresponding points are matched by the feature difference between point pairs to eliminate the wrong point pairs and solve the problems of missing data and noise interference in part of the point cloud. Finally, the mean matching distance (MMD) is used as a metric to improve the alignment accuracy. MMD is a metric to improve the ICP algorithm to align the point clouds and solve the problem of low alignment accuracy when the initial poses are poor. The experimental results show that the algorithm improves the alignment accuracy by at least one order of magnitude and saves the alignment time in the case of poor initial poses, partial data loss, and noise interference, showing significant advantages in terms of robustness and alignment accuracy.