A physics-based reliability approach calculates the probability of failure by integrating the joint probability density of the basic random variables over the failure region.The failure region is defined by a limit-state function.Because it is time consuming to numerically evaluate the probability integral, the First Order Reliability Method (FORM) is commonly used.The error of the FORM, however, may be too large because of the first order approximation.In this work, the Support Vector Machine (SVM) method is used to improve the accuracy.At first the FORM is performed to search the Most Probably Point (MPP), where the limit-state has the highest probability density at the limit state.Then random samples are drawn around the MPP.The samples are used as the training points for SVM to create a surrogate model of the limit-state function.The gradient information at the MPP is also used in the process.Then Importance Sampling is used to calculate the probability of failure with the surrogate model.The examples demonstrate that the proposed method is more accurate than the FORM and more efficient than the direct Monte Carlo simulation.