Geomembrane defect-induced leakage may cause potential hazards to an earth-rock dam with geomembrane on the dam surface used for seepage control. Therefore, three-dimensional saturated-unsaturated seepage fields with different sizes of geomembrane defects occurring at different locations on the surface of an earth-rock dam were simulated with the finite element method. The laws of variations of the entire and local seepage fields with different geomembrane defects were analyzed. The seepage behavior induced by geomembrane defects was simulated using the methods of removing defect elements and amplifying the permeability, respectively. Results show that defect-induced leakage has significant influence on the local seepage field near the defects and little influence on other parts of the dam body. With the low position of geomembrane defects, the head at defects will increase, leading to significant increases of the total seepage flow and local elevation of phreatic lines across the defects. Finally, some methods were proposed for control of defect-induced leakage in engineering design.