Estimation of vulnerability in cities situated closed to active fault needs to be carefully treated. In the near-fault area, two special features referred to as forward directivity and static deformation cause the directivity and fling pulses with long period and high amplitude, which can increase the value of strong ground motion such as peak ground acceleration, velocity and displacement. In this article, the uncertainty in seismic risk estimation of the building for the areas located in the vicinity of the active faults caused by peak ground acceleration was investigated. To this end, the building inventory of three areas (areas 1, 7 and 8) in Karaj city that are located very close to the north Karaj fault was employed. In this regard, the peak ground acceleration in these areas is calculated in two PSHA (Probabilistic Seismic Hazard Assessment) and worst scenario. Then, the risk of building damage was calculated for two cases assuming different sets of ground motions. The comparison among the estimated collapse risks shows an increase of %48 at the extensive damage state, respectively.