The approximation of seismic hazard curve H(x) affects the determination of risk-targeted design ground motion SaR significantly. The traditional first-order approximation of H(x) for obtaining SaR may result in a relatively large error. Therefore, this study employs a second-order approximation of H(x) with three parameters to define the fitted parabolic functions. Three scenarios are proposed to determine the second-order approximation of H(x). Scenario 1 utilizes the ground motion intensity values of the three points along with their corresponding annual exceedance probabilities. Scenario 2 is essentially the same as scenario 1, with the difference that scenario 2 uses the tangent of the parabola at the frequent-level earthquake when the ground motion intensity is less than that of the frequent-level earthquake. Scenario 3 involves the utilization of two points and a symmetry axis. The suitability of the three scenarios is verified by comparing the risk-targeted maximum considered earthquake (MCER) obtained from the approximated H(x) with that from the actual H(x). The suitability is further examined by studying the ground motion intensity interval which significantly affects the determination of SaR through the lower and upper integration limits. Subsequently, the maps of MCER, collapse risk, and risk coefficient (i.e., the ratio of MCER to MCE) for mainland China are developed, and the sensitivity analysis is studied. It is shown that the ranges of the collapse risk in 50 years and risk coefficients for mainland China are 0.86%–1.03 % and 0.94–1.01, respectively. Therefore, only minor adjustments to the MCE in the current Chinese seismic design code are required to achieve the target collapse risk of 1 % in 50 years. •Three scenarios are proposed for second-order seismic hazard curve approximation.•Ground motion intensity interval that significantly impacts RTGM is determined.•Sensitivity analysis for RTGM is conducted with various decision parameters.