Due to the nested optimization loop structure and time-demanding computation of structural response, the computational accuracy and cost of reliability-based design optimization (RBDO) have become a challenging issue in engineering application. Kriging-model-based approach is an effective tool to improve the computational efficiency in the practical RBDO problems; however, a larger number of sample points are required for meeting high computational accuracy requirements in traditional methods. In this paper, an adaptive directional boundary sampling (ADBS) method is developed in order to greatly reduce the computational sample points with a reasonable accuracy, in which the sample points are added along the ideal descending direction of objective function. Furthermore, only sample points located near the constraint boundary are mainly selected in the vicinity of the optimum point according to the strategy of multi-objective optimization; thus, substantial number of sample points located in the failure region is neglected, resulting in the improved performance of computational efficiency. Four numerical examples and one engineering application are provided for demonstrating the efficiency and accuracy of the proposed sampling method.