Abstarct: Earthquake is one of the natural disasters that has always influenced human life. Although it is impossible to prevent earthquakes or to predict the precise time of its occurrence, by designing earthquake resistant structures, the amount of financial damages and casualties can be reduced to some extent. Of course, this resistant design requires the use of seismic hazard analysis science, which will be possible by estimating the parameters of strong ground motion, such as acceleration, velocity and displacement in any area. It should be noted that estimating the parameters of strong ground motion will not be possible unless through obtaining the appropriate attenuation relationship. In this paper the effort is on estimating an appropriate attenuation relationship to estimate the horizontal component of Peak Ground Acceleration (PGAH) possible occurrence in each region by using the two methods of Gene exxpression Programming (GEP) and Group Method of Data Handling (GMDH) with high approximation and finally the two methods are compared. To achieve this goal, an up-to-date and extensive catalog consisting of 1185 records of earthquakes occurred around the world has been prepared and the parameters of magnitude, hypo central distance and shear wave velocity of these earthquakes have been used to obtain an attenuation relationship. Finally, the fitness function is calculated using the root mean square error (RMSE), which is obtained 765.55 from 1000 in the Gene exxpression Programming (GEP) method and 766.6 from 1000 in the Group Method of Data Handling (GMDH) method showing the high proportion of the obtained values from the final attenuation relation with measured values from the previous earthquakes in both of methods. Generally, some strength points of this study are: First of all, the widespread being of statistical population and addition of records in recent years to earthquake catalogue leads to more precise attenuation relation. Secondly, using the Gene exxpression Programming (GEP) and Group Method of Data Handling (GMDH) and comparing results.