An efficient model-order reduction technique for general RLC networks is proposed. The method is extended from the previous projection-base moment matching method by considering both the circuit network and its corresponding adjoint network. By exploring the symmetry properties of the MNA formulation, the proposed method needs only one half of the system moment information compared with previous ones. The passivity of the reduced-order model is still preserved. The relationship between the adjoint network and sensitivity analysis is also discussed. Experimental results demonstrate the accuracy and the efficiency of the method.