An improved numerical approach to analyze the flexural behavior of reinforced concrete (RC) structure under explosion is proposed in this paper. Instead of considering the layered section approach, the proposed approach is based on the moment-curvature relation of an RC section, which can significantly reduce the solution steps such as the calculation of the neutral axis and bending stiffness and facilitates the sequential collapse analysis of entire RC frame structures. The hysteretic moment-curvature relation of the RC section is constructed with reference to the hysteretic stress-strain relation of reinforcing steel, upon construction of the monotonic moment-curvature envelope curve considering the bond-slip effect, the axial force effect, and the strain rate effect. In advance, the increase of the resisting capacity by the strain rate effect is taken into consideration by redefining the dynamic increase factor (DIF) as a function of the curvature rate. The exactness of the proposed hysteretic moment-curvature relation of an RC section is verified through a comparison of the numerical results with the experimental data for RC beams and columns. Moreover, additional numerical simulations for an RC frame are performed to demonstrate that the introduced numerical approach makes it possible to trace the sequential collapse of an entire RC structure subject to blast loadings, in spite of using a limited number of finite elements.