In seismic risk assessment of bridges, developing fragility function is a fundamental step to characterize the structural vulnerability, which is usually derived based on the relationship between the engineering demand parameter (EDP) and intensity measure (IM). The EDP‐IM relationships are generally developed through three approaches, namely Cloud analysis (Cloud), incremental dynamic analysis (IDA), and multiple strip analysis (MSA). It is known that the Cloud method is computationally efficient while the IDA and MSA can provide the accurate fragility estimates. Thus, the present paper proposes an efficient and accurate fragility (EAF) approach which has similar computational demand as Cloud but keeps the same level of accuracy as IDA or MSA. In this proposed EAF procedure, the nonlinear time‐history responses at the intensifying duration of ground motions were used to develop the EDP‐IM curves. And these EDP‐IM curves are accurate enough to replace the IDA curves in developing fragility curves. To illustrate the efficiency and accuracy of the proposed EAF method, two typical bridges (a two‐span single‐frame bridge and a single‐pylon cable‐stayed bridge) were selected and modeled in OpenSees and employed as case studies. By comparing the fragility estimates of these bridges to IDA and MSA, it is demonstrated that the proposed EAF approach leads to reliable fragility results, while has similar computational time as Cloud.