To solve the structural reliability of the implicit nonlinear performance function (PF) that is complicated and changeable in the non-normal variable space, the advantages of the saddle-point approximation (SA) and line sampling (LS) were merged, and the merits of dichotomy and the solution efficiency of the golden section method were combined to propose the saddle-point approximation-line sampling (SA-LS) method based on the dichotomy of the golden section point. According to SA, it is quick to find the zero-point in PF corresponding to each sample along the important LS direction by the above dichotomy so that the structural failure probability can be transformed into the arithmetical mean of a series linear PF failure probability. This research shows that the SA-LS method based on the dichotomy of the golden section point is of high precision and fast velocity when it is used to analyze the structural reliability for implicit nonlinear PF, which are complicated, changeable and of non-normal variables.