Abstract: In this paper,the expressions of peak ground motion acceleration and r. m. s acceleration have been derived,based on the Haskell's co-cube radiated spectrum of source model,plus the terms of anelastic attenuation,geometrical spreading and enlargement factor of free surface. Then,a ground motion attenuation model depsndent on the rupture direction of the seismic source from the expressions has been recommended. The formula is as the following: In (a) = C0+ C1Mw+ C21nR+ C3R+C41n(D())+C5d()+C6S Where a is a parameter of peak acceleration or RMS acceleration for the directivity functions of D() and d(),respectively.The results of uni-magnitude regressions indicated that the model proposed in this paper is more adequate than the euqi-distance circle model,utilizing the acceleration data of the Morgan Hill and Imperial Valley earthquakes which abound with ground motion records. Standard deviations may be reduced by 0.1 to 0.2,compiring the model developed in this paper with the conventional attenuation model,for instance,the Joyner and Boore's model. The ground motion attenuation model dependent on rupture direction of seismic source developed in this paper may be applied to earthquakes with different patterns of faults,for example,to unilateral or bilateral strik-slip and dip-slip rupture and reverse rupture patterns. The inadequacy of the circle distribuation of Cornell's piont source model and the narrow-long ellipse distribua-tion of fault rupture model with equi-distance also may be improved. Finally,The formulas of PGA and RMS accelerations attenuation dependent on the rupture direction of the seismic source are presented for the Western United States.