Variational scheme is applied to study the effective nonlinear response of strongly nonlinear composite conductor with Hashin-Shtrikman (H-S) microgeometry in which both components obey the current density (J)-electrical field (E) relation of the form J = χ E 2 E, where χ is nonlinear coefficient. Two cases are discussed, our theoretical results derived numerically are compared with published simulation data and H-S lower bound as well as other estimates, a resonable agreement is found.