3D datum transformation is widely used in geodesy， photogrammetry， point cloud registration and many other fields， and there have been many studies of 3D datum transformation problems for large angles and arbitrary scales. When the observations contain gross errors， the estimated transformation parameters are adversely affected and even severely distorted. In order to deal with large-angle 3D datum transformation problems that contain gross errors， this paper first abstracts the large-angle 3D datum transformation problem as constrained least squares （CLS） problem， and derives the least-squares solutions for the parameters under orthogonal constraints. Then， a distinctive sensitivity analysis approach is introduced into this CLS problem. The local sensitivity of the weighted sum of squared residuals to the perturbations of observations in the CLS problem is discussed， and then， the local test statistics are constructed based on these sensitivity indicators， deducing a data snooping algorithm for CLS problem. Finally， simulations and experiments with real data are carried out to verify the effectiveness of the algorithm. The computational results of the simulated and real experiment show that the proposed data-snooping algorithm using the sensitivity-based test statistics can effectually decrease the negative impact of the outliers and derive reliable parameters， which effectively solves the problem of processing gross errors in large-angle 3D datum transformation.