A new hybrid method is proposed to estimate the failure probability of a structure subject to random parameters. The high dimensional model representation (HDMR) combined with artificial neural network (ANN) is used to approximate implicit limit state functions in structural reliability analysis. HDMR facilitates the lower dimensional approximation of the original limit states function. For evaluating the failure probability, a first-order HDMR approximation is constructed by deploying sampling points along each random variable axis and hence obtaining the structural responses. To reduce the computational effort of the evaluation of limit state function, an ANN surrogate is trained based on the sampling points from HDMR. The component of the approximated function in HDMR can be regarded as the input of the ANN and the response of limit state function can be regarded as the target for training an ANN surrogate. This trained ANN surrogate is used to obtain structural outputs instead of directly calling the numerical model of a structure. After generating the ANN surrogate, Monte Carlo simulation (MCS) is performed to obtain the failure probability, based on the trained ANN surrogate. Three numerical examples are used to illustrate the accuracy and efficiency of the proposed method.