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Due to the effects of the earth's rotation and the satellite's elliptical orbit, the Doppler centroid varies along the orbit in geosynchronous earth orbit synthetic aperture radar (GEO SAR). With an ultrahigh orbit height, the beam may illuminate outside the earth surface with a rotation angle large than 9 degrees. Therefore, the usual attitude steering methods to minimize the Doppler centroid in low earth orbit SAR (LEO SAR) may not be suitable for GEO SAR. In this paper, a novel steering strategy to maximize Nesigma0 for GEO SAR is proposed when the beam illuminates outside the earth surface. The new geometry and the gradient method are applied to demonstrate the method. The ability to stare imaging in geosynchronous orbit SAR is analyzed and verified by using the back projection (BP) algorithm to simulate the imaging principle. Nesigma0 under the new method improved 1dB comparing with the original image.