An earthquake produces a torsional vibration of structures with eccentricity. The torsional vibration causes large damage to structures. Authors propose a new earthquake resistant system of a non-symmetric Z-type NC braced frame with performance of earthquake response reduction. The system produces incremental torsional deformation with function of elastic response reduction. In this paper earthquake response analytical results of the NC braced frames with the eccentricity show the same level of torsional vibration as BRB frames. The system can be applied to frames with the eccentricity.