In order to correct the image distortion in the hyperspectral camera side-scan geometric Imaging, the image pixel geo-referenced algorithm was deduced in detail in the present paper, which is suitable to the linear push-broom camera side-scan imaging on the ground in any direction. It takes the orientation of objects in the navigation coordinates system into account. Combined with the ground sampling distance of geo-referenced image and the area of push broom imaging, the general process of geo-referenced image divided into grids is also presented. The new image rows and columns will be got through the geo-referenced image area dividing the ground sampling distance. Considering the error produced by round rule in the pixel grids generated progress, and the spectral mixing problem caused by traditional direct spectral sampling method in the process of image correction, the improved spectral sampling method based on the weighted fusion method was proposed. It takes the area proportion of adjacent pixels in the new generated pixel as coefficient and then the coefficients are normalized to avoid the spectral overflow. So the new generated pixel is combined with the geo-referenced adjacent pixels spectral. Finally the amounts of push-broom imaging experiments were taken on the ground, and the distortion images were corrected according to the algorithm proposed above. The results show that the linear image distortion correction algorithm is valid and robust. At the same time, multiple samples were selected in the corrected images to verify the spectral data. The results indicate that the improved spectral sampling method is better than the direct spectral sampling algorithm. It provides reference for the application of similar productions on the ground.