Description of rock morphology is of great significance to better understand the shear behavior of the discontinuities. Firstly, from the shear directional characteristics of the discontinuities, a new index SC (shear coefficient) describing discontinuities morphology is proposed based on some pivotal role on shear behavior of its morphology in the shear direction. The index describes undulation characteristics, statistical distribution of undulation and height characteristics of two-dimensional discontinuities morphology in the shear direction, and can also characterize directionality of the morphology. Moreover, the relationship between SC and JRC (joint roughness coefficient) is established based on 10 digitized JRC standard curves. Then, with the help of point cloud data of rock discontinuities obtained by three-dimensional (3D) white scanner, the shear coefficient SC is extended to 3D to better characterize 3D morphology characteristics of discontinuities. Finally, the three-dimensional shear coefficient (SC3D) is used to quantify morphology of natural rock discontinuities in different directions. It is shown that SC can well represent anisotropic morphology characteristics of discontinuities.