High-resolution imaging through strongly scattering media is a long-standing challenge with broad applications including biomedical imaging, remote sensing, navigation and so on. In the past decade, several techniques have been proposed to solve this problem. Among these techniques, speckle-correlation-based method can non-invasively extract the spectral amplitude of imaging target from captured scrambled image by conducting autocorrelation and Fourier transform operations. The imaging target can be reconstructed by iterative phase retrieval, while the imaging resolution is restricted by the low-pass property of scattering imaging system. Disproportionality of different frequency components of extracted imaging target spectral amplitude blurs the reconstruction results. In this paper, we propose the spectrum correlation approach to correct the proportional relations among low and medium frequency components of extracted imaging target spectral amplitude. By modeling the propagation of scattering wavefront and calculating the autocorrelation expectation of point spread function (PSF) at different depths, statistical spectral amplitude distribution of PSF is generated to be the weighting factor for imaging target spectrum correction. Nonlinear translation of speckle pattern spectrum expectation is introduced for error reduction in high-frequency components of extracted imaging target spectral amplitude. Finally, corrected spectral amplitude is utilized as the input of phase-retrieval algorithm for imaging target reconstruction. Simulated experiments are presented to demonstrate the effectiveness of the proposed method. After the spectrum correction of extracted spectral amplitude, imaging resolution of speckle-correlation-based scattering imaging system is improved, which can be applied to reconstruct target with smaller size or located deeper in the scattering media.