The Risley-prism imaging system (RPIS) is a powerful way to achieve bionic human eye imaging with great advantages on large field of view (FOV) and variable resolution imaging owing to the autonomous controlled deflection of light. But the imaging dispersion originating from nonlinear and uneven light deflection results in limited imaging wavelength that seriously hinders its application. The existing solutions for imaging dispersion mainly rely on the hardware, which generally has bulky structure and limited improvement on image. Besides, the existing image evaluation methods for dispersion are not suitable for RPIS due to inhomogeneous dispersion. Herein, this paper systematically analyzes the mechanism and characteristics of dispersion in the RPIS, and proposes a cooperative correction method for image distortion and dispersion of multiple-color imaging, achieving the elimination of distortion and dispersion simultaneously without changing the optical structure. A dispersion evaluation index based on Pearson's correlation coefficient (PCC) is also established, and the objectivity and validity of the index are proved by experiments. Furthermore, a kind of compact RPIS based on an RGB camera is built, and both indoor and outdoor experiments are conducted. The experimental results demonstrate that proposed algorithm has strong universality and robustness for various scenes and targets.