The shape of core-stones remained in the weathering basalt column is an index to classify its weathered degree. In this paper, a roundness index (RI) like the box dimension using in fractal theory, was employed to quantitatively measure the shape of core-stone in various weathering grades. The rounded core-stone that is weathered seriously has a smaller RI value. According to the value of RI, the five classes shown in the Russell–Taylor–Pettijohn chart for visually classifying grain shape is available to approximately determine the weathered grades of core-stones remained in the basalt column in Taiwan. A slump test is preliminarily tested to show the difference in repose angle of a stability slope assembled by the grains in a similar shape. The collection of angular core-stones those are less weathered (with a higher RI value) indeed reveals a greater repose angle.