Traditional airborne SAR （Synthetic Aperture Radar） makes use of the GPS/INS to compensate the platform motion error to acquire high resolution images. GPS data with geographical coordinates （consists of longitude

latitude and height） is converted to a local Cartesian coordinates

under which raw radar data is processed with some imaging and motion compensation algorithms to create an image with the local coordinates. However

it is not easy to be understood for other departments who need an image located by geographical coordinates. This paper presents a novel SAR imaging algorithm derived from Back-Projection that can be processed directly under the geographical coordinates and avoid coordinates transformation. Each pixel of the im- age obtained via this algorithm is located with geographical coordinates

which is convenient to be applied by the intelligence or other survey departments. Images obtained under geographical coordinates by this algorithm are as clear as traditional algorithms that been proved by simulations and an outside experiment.