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For reliability-based design optimization (RBDO), generating an input statistical model with confidence level has been recently proposed to offset the inaccurate estimation of the input statistical model with Gaussian distributions. To do this, the confidence intervals of mean and standard deviation are calculated using the Gaussian distributions of input random variables. However, if the input random variables are non-Gaussian, use of the Gaussian distributions of input variables will provide inaccurate confidence intervals and will yield an undesirable confidence level of the reliability-based optimum design meeting the target reliability. In this paper, the RBDO method using the bootstrap method, which does not use the Gaussian distributions of input variables to calculate the confidence intervals of mean and standard deviation, is proposed to obtain the desirable confidence level of output performance for non-Gaussian distributions.