The traditional hyperbolic range equation model will produce large errors in the spaceborne sliding spotlight synthetic aperture radar with large azimuth time. Although the equivalent acceleration range model (EARM) can deal with the problem of large azimuth scenes well, the interpolation steps from azimuth resampling make the computational burden of algorithm very huge. In response to this problem, this paper improves EARM by dividing the range model into two parts: residual terms of azimuth time and equivalent range expression. The frequency domain imaging algorithm designed for the new range model omits the interpolation step of azimuth resampling. The simulation experiments verify the efficiency and validity of the proposed methodology.