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Based on the ground surface perturbation concept, a novel stopband-enhanced electromagnetic-bandgap (EBG) structure has been proposed to suppress the power/ground noise on a three-layer package. This structure consists of a coplanar periodic pattern on the top layer, a ground plane on the third layer, and a ground surface perturbation lattice on the second layer with eight vias connecting to the ground plane. By designing the dimension and via numbers, the ground surface perturbation lattice can significantly enhance the stopband bandwidth. A generic 1-D circuit model is proposed for the three-layer EBG structure. The reason why the proposed structure can possess wider stopband will be explained. Several test samples are fabricated. The agreement of the stopband between the circuit model and measured results are good.