We propose a novel method for matching two sparse point-sets of identical cardinality with distribution similarity. The point-sets are extracted from two subjects with underlying non-rigidity and non-uniform scaling, one being a model set with point identity and the other representing the observed data. There exists neither a global nor local affine transformations between the point-sets. To establish a one-to-one match, we introduce a new similarity K-dimensional tree, which is well adapted and robust to such data. We construct a similarity K-d tree for the model set. Then a corresponding tree of the data set is constructed following the structure information embedded in the model tree. Matching sequences of the two point sets are generated by traversing the identically structured trees. Experimental results based on the synthetic data analysis and real data confirm this method is applicable for robust spatial matching of sparse point-sets under non-rigid distortion.