Abstract: This paper computed the generalized fractal dimension structure of the water radon observational data for 7 stations in Hebei, Tianjin and Beijing, using the basis theory in the fractional form and dimension. From the computed generalized fractal dimension curves for the 7 stations in 1972-1978, it can be seen that, before the Tangshan M7.8 earthquake in July 1976, the data from 5 stations showed obvious dimension decrease, that from the other two stations were not obvious, and the generalized fractal dimention values of two stations still showed decrease after the earthquake. The result shows that the decreases of the generalized fractal dimension structure before earthquakes can provide reliable basis for earthquake prediction.