The integer transform methods are widely adopted in international image and video coding standards because of its fast calculation speed. The existing integer transform methods based on the continuous orthogonal function system not only struggle to obtain the exact integer form of the original transform, but also fails to overcome the Gibbs oscillation phenomenon in the discontinuous signal representation, thus reduces the reconstructed image quality. This paper proposed a new integer transform algorithm and its image compression method based on discontinuous orthogonal U-system. Firstly, the piecewise integration and the Gram-Schmidt process were used to calculate the two-dimensional orthogonal matrix of the U-system, and the scaling factors of row vectors were extracted to obtain the integer matrix. Secondly, the reversible integer U transform was established and the integer matrix was applied to concentrate the energy of images into a small amount of data sets, while merging scaling factors with quantization to reduce computational burden. Then, the fast integer U transform was achieved by using matrix decomposition and sparse matrices. Finally, the integer U transform module and inverse transform module were designed to alleviate the pressure of image storage and transmission. Experimental results show that the proposed method can reduce truncation errors of reversible image transform compared with related algorithms; the new method obtains higher compression image quality in image and video compression experiments, and the fast transform algorithm effectively saves computational time.