The conventional mean shift algorithm has been known to be sensitive to selecting a bandwidth. We present a robust mean shift algorithm with heterogeneous node weights that come from a geometric structure of a given data set. Before running MS procedure, we reconstruct un-normalized weights (a rough surface of data points) from the Delaunay Triangulation. The un-normalized weights help MS to avoid the problem of failing of misled mean shift vectors. As a result, we can obtain a more robust clustering result compared to the conventional mean shift algorithm. We also propose an alternative way to assign weights for large size datasets and noisy datasets.