A lumped-LC equivalent circuit to model a novel rectangular bracket shaped defected ground structure (DGS) is presented in this paper. The presented equivalent circuit can accurately predicate the frequency responses, in terms of the magnitude and phase responses of S parameters, of the studied DGS. The lumped LC parameters of the presented model are extracted based on a unit cell of the DGS. Further, the model is found to be applicable in microwave engineering, including microwave filter designs. Some design examples are presented and examined. The studied DGS based microwave filters characterize maximum passband flatness, sharp skirt between the passband and stopband and wide stopband. The studied equivalent circuit model can accurately predicate the frequency responses including the magnitude and phase of S parameters.