An extended nonlinear chirp scaling (NLCS) algorithm is proposed to process data of highly squinted, high-resolution, missile-borne synthetic aperture radar (SAR) diving with a constant acceleration. Due to the complex diving movement, the traditional signal model and focusing algorithm are no longer suited for missile-borne SAR signal processing. Therefore, an accurate range equation is presented, named as the equivalent hyperbolic range model (EHRM), which is more accurate and concise compared with the conventional fourth-order polynomial range equation. Based on the EHRM, a two-dimensional point target reference spectrum is derived, and an extended NLCS algorithm for missile-borne SAR image formation is developed. In the algorithm, a linear range walk correction is used to significantly remove the range-azimuth cross coupling, and an azimuth NLCS processing is adopted to solve the azimuth space variant focusing problem. Moreover, the operations of the proposed algorithm are carried out without any interpolation, thus having small computational loads. Finally, the simulation results and real-data processing results validate the proposed focusing algorithm.