Compressive hyperspectral imaging technology can quickly detect the encoded two-dimensional measurements and reconstruct the three-dimensional hyperspectral images offline, which is of great significance for object detection and analysis. To provide more information for reconstruction and improve the reconstruction quality, some of the latest compressive hyperspectral imaging systems adopt a dual-camera design. To utilize the information from additional camera more efficiently, this paper proposes a residual image recovery method. The proposed method takes advantage of the structural similarity between the image captured by the additional camera and the hyperspectral image, combining the measurements from the additional camera and coded aperture snapshot spectral imaging (CASSI) sensor to construct an estimated hyperspectral image. Then, the component of the estimated hyperspectral image is subtracted from the measurement of the CASSI sensor to obtain the residual data. The residual data is used to reconstruct the residual hyperspectral image. Finally, the reconstructed hyperspectral image is the sum of the estimated and residual image. Compared with some state-of-the-art algorithms based on such systems, the proposed method can significantly improve the reconstruction quality of hyperspectral image.