The spatial distribution of acoustic emission (AE) events in the failure process of several rock specimens was acquired using an advanced AE acquiring and analyzing system. The box counting method (BCM) was employed to calculate the fractal dimension (FD) of AE spatial distribution. There is a similar correlation between the fractal dimension and the load strength for different rock specimens. The fractal dimension presents a decreasing trend with the increase of load strength. For the same kind of specimens, their FD values will decrease to the level below a relatively same value when they reach failure. This value can be regarded as the critical value, which implies that the specimen will reach failure soon. The results reflect that it is possible to correlate the damage of rock with a macroscopic parameter, the FD value of AE signals. Furthermore, the FD value can be also used to forecast the final failure of rock. This conclusion allows identifying or predicting the damage in rock with a great advantage over the classic theory and is very crucial for forecasting rockburst or other dynamic disasters in mines.