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Many of engineering problems have nonlinear or highly nonlinear limit state functions. Different approaches have been developed in calculating of failure probability in these problems. These methods calculate failure probability by generating random samples with a specific distribution. The Monte Carlo is one the most efficient and applicable method among these approaches. However, this method has some problems including need to calculating of variable distribution function parameters and inverse cumulative density function of variables. In order to solve these deficiencies, in the present research, an efficient method for generating samples is presented. Additionally, enhancing performance of Monte Carlo method and more accurate results by minimum computational cost for functions with very low failure probability can be regarded as other advantages of the proposed method. For evaluating performance of the proposed method, four engineering problems have been investigated and the obtained results for calculating of failure probability have been compared with available methods. By applying the proposed method, such main steps can be neglected and stable results with high accuracy can be gained in comparison with traditional methods in lower sample numbers too.