This paper analyzes an innovative geographically referenced (GR) stripmap mode for the airborne synthetic aperture radar (SAR). In the GR stripmap SAR, the antenna beam illuminates orthogonally with the ground strip, which is not parallel to the SAR trajectory. Benefiting from the GR stripmap mode, the effective observation swath can be enlarged comparing to what can be realized by the traditional stripmap SAR. A modified nonlinear chirp scaling (MNLCS) method is suggested for the GR stripmap SAR imaging. It can solve the problem caused by scatterers' non-uniform Doppler history that disables most traditional imaging algorithms for the GR stripmap SAR. The MNLCS algorithm consists of three main steps. First, a bulk range migration compensation procedure eliminates the linear range migration (range walk). Second, an azimuth perturbation filter unifies the Doppler frequency modulation rate for each range cell. Lastly, a modified chirp scaling processing finishes the data focusing. Performance of the MNLCS algorithm was analyzed, followed by a series of computer simulation results, which validated the MNLCS for the GR stripmap SAR imaging.