Based on extensive and thorough observation of a large amount of geographical, geological and economic phenomena such as coastline, earthquake, stock etc, Mandelbrot discovered the inherent character in nature that he called fractal, and he also considered the fractal dimension as the quantitative parameter to describe numerous irregular phenomena in nature. As a new tool to picture the complexity of nature, the fractal theory has been widely used in many fields. As to the study of fault, it has made progress in many fields such as the fractal character, the spatial distribution model, movement, classification, calculation of fractal dimension of fault, the relation between fault and earthquake, the fractal character of rock, and scaling between short and large fault, etc. Researches on the fractal dimensions of China's faults, the prediction of dynamic change, have not been attempted till now. These questions are discussed in this paper.
    Based on the fractal theory and grey theory, the fractal character of faults of China has been quantitatively analyzed in this paper. Firstly, fractal dimensions of faults of China's mainland are calculated and compared. The fractal dimension of the whole faults of China's mainland is 1.7682, with active faults is 1.5989, and 1.6755 for less active faults. The fractal dimension of faults of the Qinghai Tibet Plateaus the largest in eight natural regions of China. Secondly, relationship of fractal dimensions between faults and mountains is discussed, and the quantitative relationship between faults and mountains is established. Thirdly, fractal dimensions of faults of China's mainland in different geological periods are calculated, and grey forecast models of fractal dimensions are established, too. It indicates that the fractal theory and grey theory are useful to the study of the characteristics of faults. The fractal dimension of faults of China's mainland for next geological periods may be 1.5995, and the complexity of faults will be increased correspondingly.