The conventional monostatic synthetic aperture radar (SAR) shows a limitation if a forward-looking geometry is used. However, bistatic forward-looking SAR gives a good solution, providing a high resolution image in the flight path direction. Due to the fact that the range history of bistatic SAR is a double square root, classical imaging algorithm cannot be applied to the bistatic SAR directly. Also it is difficult to deduce imaging algorithm from double square root directly. The hyperbolic approximating method can transform double square root into single one, when being used in forward-looking geometry, and the high order term error is obvious and cannot be ignored. In this paper, we propose a modified hyperbolic approximating method, which makes a cubic term approximation and improves the precision, then we apply the new method to bistatic forward-looking SAR and deduce the bistatic point spectrum. Based on the spectrum, a modified range Doppler algorithm is proposed for focusing bistatic forward-looking SAR. Finally, numerical simulation is used to compare the original hyperbolic approximating method with the modified one for veridating the proposed algorithm and processing approach.