Conventional synthetic aperture radar(SAR) systems cannot achieve both highresolution and wide-swath imaging simultaneously.This problem can be mitigated by employing multiple-azimuth-phases(MAPs) technology for spaceborne sliding spotlight SAR systems.However, traditional imaging algorithms have met challenges to process the data accurately, due to range model error, MAPs data reconstruction problem, high-order cross-coupling phase error and variation of Doppler parameters along the azimuth direction.Therefore, an improved imaging algorithm is proposed for solving the above problems.Firstly, a modified hyperbolic range equation(MHRE) is proposed by introducing a cubic term into the traditional hyperbolic range equation(THRE).And two curved orbit correction methods are derived based on the proposed range model.Then, a MAPs sliding spotlight data reconstruction method is introduced, which solves the spectral aliasing problem by a de-rotation operation.Finally, high-order cross-coupling phases and variation of Doppler parameters are analyzed and the corresponding compensation methods are proposed.Simulation results for point-target scene are provided to verify the effectiveness of the proposed algorithm. Conventional synthetic aperture radar (SAR) systems can not achieve both high resolution and wide-swath imaging. This problem can be mitigated by employing multiple-azimuth-phases (MAPs) technology for spaceborne sliding spotlight SAR systems. Despite, traditional imaging algorithms have met challenges to process the data accurately, due to range model error, MAPs data reconstruction problem, high-order cross-coupling phase error and variation of Doppler parameters along the azimuth direction. Before, an improved imaging algorithm is proposed for solving the above problems. Firstly , a modified hyperbolic range equation (MHRE) is proposed by introducing a cubic term into the traditional hyperbolic range equation (THRE). End two curved orbit correction methods are derived based on the proposed range model. Chen, a MAPs sliding spotlight data reconstruction method is introduced, which solves the spectral aliasing problem by a de-rotation operation. Finally, high-order cross-coupling phases and variation of Doppler parameters are analyzed and the corresponding compensation methods are proposed. Simulation results for point-target scene are provided to verify the effectiveness of the proposed algorithm.