Sandy Dolomite is a kind of widely distributed rock. The uniaxial compressive strength (UCS) of Sandy Dolomite is an important metric in the application in civil engineering, geotechnical engineering, and underground engineering. Direct measurement of UCS is costly, time-consuming, and even infeasible in some cases. To address this problem, we establish an indirect measuring method based on the convolutional neural network (CNN) and regression analysis (RA). The new method is straightforward and effective for UCS prediction, and has significant practical implications. To evaluate the performance of the new method, 158 dolomite samples of different sandification grades are collected for testing their UCS along and near the Yuxi section of the Central Yunnan Water Diversion (CYWD) Project in Yunnan Province, Southwest of China. Two regression equations with high correlation coefficients are established according to the RA results, to predict the UCS of Sandy Dolomites. Moreover, the minimum thickness of Sandy Dolomite was determined by the Schmidt hammer rebound test. Results show that CNN outperforms RA in terms of prediction the precision of Sandy Dolomite UCS. In addition, CNN can effectively deal with uncertainty in test results, making it one of the most effective tools for predicting the UCS of Sandy Dolomite.