The expensive computational cost is always a major concern for reliability-based design optimization (RBDO) of complex problems. The performance of RBDO can be lowered by the inaccuracy of reliability analysis (RA) which is caused by multiple local optimums and multiple design points in highly non-linear space. In order to reduce the computational burden and guarantee the accuracy of RA (and thus to improve the RBDO performance), a global RBDO algorithm by adopting an improved constraint boundary sampling (GRBDO-ICBS) method is proposed. Specifically, the GRBDO-ICBS method first narrows the concerned search region by using a Kriging-based global search. The accuracies of the design points are verified by the expected risk function (ERF), and the corresponding inaccurate design points are added into training samples to update Kriging. Then a multi-start gradient-based sequential RBDO is carried out, which tries to find out all multiple design points in the concerned search region. The performance of GRBDO-ICBS is demonstrated by four examples. All results have shown that the proposed method can achieve similar accuracy as Monte Carlo simulation (MCS)-based RBDO but with a much lower computational cost.