Abstract: The CT image and value do not change obviously before the macro-failure under triaxial compression experiments on rock during damage accumulation, so it is difficult to analyze accurately the damage information only through the change of CT number. In order to identify the damage information and critical failure characteristics of sandstone, the CT image is partitioned, and the change of grey level on the position line is used to represent the change of the gray level in the subarea. The grey value curve is a rough curve representing grey change of a certain location online in the CT image. It is used to describe quantitatively the rules of sandstone damage by fractal R_d index, the damage variable is defined as the sum of R_d value of all the position line in the CT image, and it reflects the damage degree of rock. The calculated results show that when the load is about 0.84, the value of R_d has obvious fluctuations and the damage variable increases rapidly, which denotes that the damage has entered a phase of accelerated development, and the rock is in a critical damage state. The proposed method can be used to predict reasonably the damage and failure of rock.