In engineering applications of sampling-based reliability-based design optimization (RBDO), the Monte Carlo simulation (MCS) using a surrogate model of the performance function is mainly used for the probability of failure calculation and sensitivity analysis. However, if an inaccurate surrogate model is used, the calculation result using MCS will also be inaccurate, so it is essential to improve the accuracy of the surrogate model using sequential sampling. Hence, various sampling-based RBDO methods and sequential sampling methods have been proposed and used in various fields, and space mapping may also be a new framework for sequential sampling. In this paper, sampling-based RBDO with the Gaussian process regression (GPR) and space mapping is proposed. Space mapping generally attempts to utilize high-fidelity samples to update the low-fidelity model in multi-fidelity model conditions. However, in the proposed method, it is used for sequential sampling to improve the accuracy of the existing surrogate model. The major advantage of the proposed space mapping-based RBDO is that the existing surrogate model and the finally updated surrogate model can be formulated with simple matrix and vector calculations. In particular, when there is only a surrogate model that has been built due to the loss of existing sample information since the space mapping updates the model, the accuracy of the surrogate model can be improved by sequential sampling. The proposed method is compared with sequential sampling-based RBDO using GPR, and the calculation accuracy and efficiency are demonstrated through a 2D highly nonlinear example and an engineering problem.