Abstract: A new method for determining the fractal dimension by STM at nanometer scale has been proposed.Weierstrass-Mandelbrot fractal curves were used to verify the accuracy and reliability. The Computer simulation showed that fractal dimension obtained with this method generally outran the traditional yard method. The new method has been applied to the fractal dimension determination of the fractures of Ti₃Al and Ti-24Al-11Nb alloys. The results show that the fractal dimension of Ti-24Al-11Nb alloy is higher than that of Ti₃Al, and it varies with the crack extending orientation.