A new approach was developed for inverse modeling of the transient groundwater flow in dam foundations. The objective function was constructed by using both the hydraulic head and discharge time series measurements, with a weight coefficient to ensure the same magnitudes of the relative error terms. The proposed inverse modeling procedure takes advantage of the orthogonal design, forward modeling of the transient seepage flow with the finite element method, back propagation neural network and genetic algorithm, which significantly reduces the computational cost, improves the uniqueness and reliability of the inversed results and makes tractable the large-scale inverse problems in engineering practices. The proposed method was applied to back calculate the hydraulic conductivities of foundation rocks and seepage-proof barriers of Changheba gravelly clay-cored rockfill dam, where a serious foundation leak took place during its early construction stage. The inverse modeling results were validated by field measurements, and clarified the origin and the channels of the foundation leak, the permeability of the foundation rocks as well as the influences of the leakage on the long-term operation of the dam.