The main subject of the essay is study of ferroresonance in the voltage transformers at 400 kV GIS substation. Ferroresonance has destructive effects such as, undulations of high voltages, warming of transformers, increasing of heat, temperature increasing and damaging voltage transformers, high noise due to evolution due to magnet and bad working of protective instruments. So we have to apply limitations on system parameters to avoid such an undesirable phenomenon like this. In this study ferroresonance phenomenon on VTs of real GIS substation (karon 4 power plant had been studied. With regarding high risk of ferroresonance due to studied substation conditions, damping circuit (FDSD, ZD) had been designed with help of EMTP-RV and the results are presented in two conditions of being without damping and by using of damping in the circuit. The results show damping circuit is successful in obviation of these dangerous oscillations.