Abstarct: This paper aims to find optimum topology of structures so that the reliability index is maximized while a certain amount of material is used. In previous studies on Reliability baxsed Topology Optimization (RBTO), reliability index is considered as a constraint and the weight is minimized. In this research, first-order reliability method is used to calculate reliability index, in which limit state function is approximated linearly with first-order Taylor series expansion and by using an iterative method, the reliability index is determined. For structural analysis, the method of isogeometric analysis is utilized. In this method, Non-Uniform Rational B-Splines (NURBS) basis functions are used to model the exact geometry and approximate the unknown deformation field with high precision. Also, an isogeometrical level-set method is employed to optimize topology of the structure. In this method, boundaries of a structure is specified by an intersection of a hyper-surface, defined over the design domain and the boundaries are evolved by solving the so-called Hamilton-Jacobi (H-J) equation. Several examples are presented to demonstrate the efficiency and accuracy of the method. Also, optimum topologies with maximum reliability index are compared with the deterministic outcomes and also with the results when the weight is minimized under a reliability constraint.