One of the most challenging obstacles to overcome when implementing reliability-based design optimization (RBDO) is the intensive computational demand of the reliability analysis. Among the many reliability analysis techniques, the enhanced dimension reduction (eDR) method is known to have a high efficiency. While the goal is to generate an accurate and efficient reliability analysis using the smallest possible number of sampling points, it is difficult to determine such a number a priori since it mostly depends on the nonlinearity of the constraint to be approximated and the degree of uncertainty in the design factor along which we want to integrate. In order to resolve this issue, an eDR method with variable sampling points is proposed in this work. The main idea of the suggested method is to employ a different number of axial sampling points for each random design factor. We first use three sampling points for each random variable and employ the proposed criteria to decide whether or not to increase the number of sampling points. This notion of employing variable sampling points increases the efficiency of the conventional eDR method without sacrificing accuracy. In order to evaluate the performance of RBDO using the suggested reliability analysis method, the proposed scheme is applied to mathematical and engineering RBDO problems and the results are compared with those obtained using both the conventional eDR method with fixed sampling points and the performance measure approach (PMA) method. The results of the comparison clearly demonstrate that RBDO using the suggested reliability analysis method is superior to conventional methods in terms of accuracy and efficiency.