•A new probabilistic assessment framework is proposed to evaluate the failure probability of structures under blast loads.•The accuracy and efficiency of the proposed framework is verified by the direct Monte Carlo simulation method.•Collapse risk of a 10-story steel frame under VBIED is analyzed.•The effective measures in protecting structures are determined based on the results of reliability analysis. This study investigates the failure probability of steel frame structures against terrorist attack from Vehicle Borne Improvised Explosive Device (VBIED). A two-step approach is used to evaluate the collapse potential of structures against blast loads. In the first step, the damage degree and responses of structural members under blast loads are determined based on an equivalent single–degree of freedom system. In the second step, the post-blast collapse behavior of steel frame structures is investigated using a 3-D nonlinear macro-based numerical model. To improve the computational efficiency, the failure probability is calculated using subset simulation method cooperated with an advanced Delayed Rejection Adaptive Markov Chain Monte Carlo simulation algorithm. The variability of blast load, vertical gravity load and structural material properties are considered. The computational framework is applied to a prototype 10-story steel frame to study the failure risk against VBIED. The results show that the reliability assessment framework used in this study provides an accurate and more efficient prediction of failure risk of structures against blast loads compared with the direct Monte Carlo simulation method. The framework also presents an approach for determination of effective measures in protecting structures against blast loads.