The analysis of dominant orientations of discontinuities is a fundamental work for a further evaluation of the stability of rock mass. By traditional plot methods such as isopycnic diagram and rose diagram, we can only obtain a simple classification of the orientations, but the exact dominant orientations of every set cannot be acquired. An improved K  means clustering algorithm is proposed. The orientations of discontinuities are represented by their unit normal vectors, and the included acute angle between two discontinuities is taken as their similarity measure. Data investigated from a rock slope of a quarry is used as a case study. The results of K  means clustering algorithm are reliable and reasonable. This method can give the accurate dominant orientations of every set.