Despite the numbers of destructive earthquakes and losses that had happened, there's a need for a tool which shows relation between damage level and earthquake intensity. Fragility curves provide this tool. In order to measure the damage, damage indexes can be defined in a way to correspond to the failures. These damages can be related to the fragility curves of earthquake severity. These curves actually determine the probability of exceedance of damage index from a limited amount based on different intensities. These curves are mainly produced by analyzing time history and different scales. The endurance time method solved the problems of scaling and longtime analyzing process by using specific accelerograms. In this research fragility curves has drawn up using time history method for 4 and 8 stories eccentrically braced frames. The results show that, in incremental dynamic analysis, the amount of acceleration corresponding to the probability of passing the IO surface from 100% for frames 4 and 8 floors is 1.32 and 0.96 respectively. Also, the spectral acceleration for the probability of passing the LS level from 100% for the same frames is 1.56 and 1.52, respectively. This value is estimated to be 2.2 and 1.76 for the CP level of 100%, for frames 4 and 8, respectively.