The 4f coherent imaging system with phase object (PO) is a new method to measure the third-order optical nonlinearity. Only the PO with uniform phase retardation is used in nonlinear-imaging technique with a PO (NIT-PO) until now. A uniform PO can only produce a single phase contrast signal. Using positive-negative PO, the sensitivity of NIT-PO can be increased. In order to increase the sensitivity of NIT-PO further with positive-negative PO, theoretical investigation about the effects of radius and phase shift of positive-negative PO on the sensitivity of the 4f coherent imaging system is made. The results show that the sensitivity of the system increases with the ratio of PO radius and the aperture radius decreasing. When the size of the PO radius unchanges, the highest sensitivity for nonlinear refraction measurement can be gotton at the position with the phase change of 0.43π.