Sedimentological analysis of grain fabric has paid scant attention to grain shape. However, the information of grain orientation is inseparable from that of shape in three-dimensional fabric analysis. Not only should the dominant major-axis orientations be recognized, but so should the dominant combinations of shapes and orientations of grains. The aim of this paper is to demonstrate that such combinations can be identified by density-based cluster analysis in a five-dimensional parameter space, where a point represents a specific combination of the shape and orientation of a grain approximated by a triaxial ellipsoid. We tested the present method using an artificial data set. The data were successfully classified into correct groups. Next, we applied it to a data set obtained by X-ray computed microtomography from some 5000 sand grains deposited in an experimental flume. We show that triaxial grains, which have principal axes with distinctive radii, have major axes in the paleocurrent orientation and roller-shaped grains in the transverse orientation. Both grain types have vertical minor axes. Those orientations are not preconditioned for statistical analysis but are recognized as significant; this suggests the potential of the method in three-dimensional fabric analysis for applications in sedimentology. The method can be applied to the statistical processing of ellipsoidal objects including, for example, deformed grains, stress ellipsoids, and magnetic susceptibility ellipsoids.