Benefiting from ultra-high angular resolution, differential wavefront sensing (DWS) technique is widely used in gravitational wave detection missions for suppressing the laser pointing jitter as well as sensing jitter of the test mass. However, the zero-offset property of the DWS which leads to absolute angular measurement error is rarely mentioned in previous researches. In this paper, we describe the mechanisms causing the DWS zero-offset with an analytical model as well as numerical method. With the analytical results, we analyze the static pointing error of the gravitational wave detection satellite induced by the DWS. As the error is far larger than the requirement of 10 nrad magnitude, a zero-offset reduction scheme is proposed. We also construct an experiment system for verifying the theoretical results. The experimental results show that the DWS zero-offset can be effectively suppressed with the proposed scheme.