This paper presents a new efficient sequential sampling approach, referred to as maximum confidence enhancement (MCE) based sequential sampling, for failure probability analysis and design optimization using surrogate models. In the proposed approach, the ordinary Kriging method is adopted to construct surrogate models for all constraints and thus Monte Carlo simulation (MCS) is used to estimate reliability and its sensitivity with respect to design variables. A cumulative confidence level is defined to quantify the accuracy of reliability estimation using MCS based on the Kriging models. To improve the efficiency of proposed approach, a maximum confidence enhancement based sequential sampling scheme is developed to update the Kriging models based on the maximum improvement of the defined cumulative confidence level, in which a sample that produces the largest improvement of the cumulative confidence level is selected to update the surrogate model. A case study is used to demonstrate the efficacy of the proposed sequential sampling methodology.