Abstract: Aiming at the reliability index calculation of a strong nonlinear structural performance function, the numerical sampling and regression analysis methods are introduced to analyze the second-order expansion of a modified performance function. Thereby the form of general law between SOSM reliability index #x003b2;_SORM and FOSM reliability index #x003b2;_FORM is obtained. On the basis of a regression analysis-prediction algorithm, a new reliability analysis method is presented according to the general law above and the application of a line sampling Monte Carlo method. Through the regression analysis of certain sampling points, the proposed algorithm can establish the specific expression of a general law between #x003b2;_SORM and #x003b2;_FORM. And the high precision solution of a strong nonlinear performance function reliability index can be achieved. The study results show that a cumbersome calculation and an inefficient iteration can be alleviated effectively by the present algorithm. The advantages of the present method in accuracy, application scope and calculation stability are obvious. Because of its convenience and intuition, the present algorithm is easy to be mastered by general designers and applied to an actual engineering analysis.