The effect of forward directivity is one of the important features of near-fault ground motions, resulting in obvious velocity pulse components in the direction perpendicular to the fault, causing serious damage to structure. In order to investigate the damage degree of the reinforced concrete frame structure under this type of special ground motion, seismic fragility analysis of a 12-story frame structure was carried out based on the traditional incremental dynamic analysis，in which structure-ground motion samples considering uncertainty of material and uncertainty of inputting ground motion were constructed. Damage state probability of the structure was calculated, combined with the empirical value of the earthquake damage index in the seismic damage assessment of the group structure, the fragility index of frequent earthquake, fortification earthquake and rarely earthquake were obtained. Results show that the reinforced concrete frame structure designed according to the seismic code under near-fault forward directivity ground motions can satisfy the seismic fortification target of “no damage under frequent earthquake”, “no unrepairable damage under design-based earthquake” and “no collapse under maximum consider earthquake”. In particular, under the action of a strong earthquake, the structure is still in a state of moderate damage with enough margin before collapse.