In super-finishing by cubic boron nitride (CBN) stones, it is considered that chips are formed by crossing of grain loci. Thus, crossing angles of grain loci are paid attention to as an important parameter. In this paper, the new method for prediction of cutting performance is proposed using average crossing angle of grain loci. On the other hand, chip formation process is classified into two types. Therefore, all crossing angles are calculated after considering these types of crossing of grain loci. Average crossing angle is defined as the mean value of those. Moreover, the relation between these average crossing angle and cutting performance is investigated by various calculations and experiments. As results, average crossing angle is one of the most important parameters to estimate the cutting performance on super-finishing using CBN stones.