3D feature descriptors provide essential information to find given models in captured scenes. In practical applications, these scenes often contain clutter. This imposes severe challenges on the 3D object recognition leading to feature mismatches between scenes and models. As such errors are not fully addressed by the existing methods, 3D feature matching still remains a largely unsolved problem. We therefore propose our Histograms of Gaussian Normal Distribution (HGND) for capturing salient feature information on a local reference frame (LRF) that enables us to solve this problem. We define a LRF on each local surface patch by using the eigenvectors of the scatter matrix. Different from the traditional local LRF-based methods, our HGND descriptor is based on the combination of geometrical and spatial information without calculating the distribution of every point and its geometrical information in a local domain. This makes it both simple and efficient. We encode the HGND descriptors in a histogram by the geometrical projected distribution of the normal vectors. These vectors are based on the spatial distribution of the points. We use three public benchmarks, the Bologna, the UWA and the Ca' Foscari Venezia dataset, to evaluate the speed, robustness, and descriptiveness of our approach. Our experiments demonstrate that the HGND is fast and obtains a more reliable matching rate than state-of-the-art approaches in cluttered situations.