The curved trajectory can lead to severely 2-D spatial-variance in spaceborne synthetic aperture radar (SAR). The azimuth-variance makes the traditional frequency domain imaging algorithms for the straight trajectory based on the assumption of azimuth translational invariance invalid. To correct the severely 2-D spatial-variance in curved trajectory spaceborne SAR, this paper studies a frequency imaging algorithm based on an optimal linear range walk correction (LRWC) preprocessing and 2-D singular value decomposition (SVD). Before the correction of the 2-D spatial-variance, an optimal LRWC preprocessing is introduced to minimize the azimuth-variance. Subsequently, a range block-SVD is proposed to correct the range-variance and, thus, achieves the accurate range cell migration correction. Finally, the azimuth tandem-SVD method is used to correct the azimuth-variance and, thus, accomplishes the azimuth compression for the whole azimuth scene. Processing of the simulated data validates the effectiveness of the proposed algorithm.