It is difficult to estimate the Doppler frequency and modulating rate for airborne SAR by using traditional vector method due to instable flight and complex terrain. In this paper, it is qualitatively analyzed that the impacts of POS, DEM and their errors on airborne SAR Doppler parameters. Then an innovative vector method is presented based on the range-coplanarity equation to estimate the Doppler centroid taking the POS and DEM as auxiliary data. The effectiveness of the proposed method is validated and analyzed via the simulation experiments. The theoretical analysis and experimental results show that the method can be used to estimate the Doppler centroid with high accuracy even in the cases of high relief, instable flight, and large squint SAR.