A new response surface method for predicting the failure probability of structural or mechanical systems subjected to random loads and material properties is presented in this paper. The method involves high dimensional model representation (HDMR) technique in conjunction with moving least squares to approximate the original implicit performance function with an explicit performance function. HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. It is a very efficient formulation of the system response, if higher-order variable correlations are weak, allowing the physical model to be captured by the first few lower-order terms. Once the response surface form is defined, the failure probability can be obtained by statistical simulation. Results of seven numerical examples involving mathematical functions and structural mechanics problems indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure.