For regions without adequate strong ground motion records, a method is developed to establish strong ground motion attenuation relationships, based on the stochastic method. Sendai area of Japan is selected as the target, since there are enough data from seismographic observation for calculation, and those from strong ground motion observation and some empirical relationships for result testing. Three parameters related to regional source and crustal medium are inversed by the micro-Genetic Algorithm. Total of 240 records from 77 small events, recorded by F-net, are adopted for the inversion. Fourier spectra are adopted as the objective function. These parameters are then taken into the stochastic method to estimate PGA. The regional ground motion attenuation relationships are compared with some strong ground motion records from K-NET and some empirical relationships to illustrate the reliability of this method.