This paper is aimed at the development of an approach of applying the curvelet transform to images of prostatectomy pathological specimens of critical Gleason grades for computer-aided classification. A set of Tissue MicroArray (TMA) images from the Johns Hopkins University have been used as the data base. We utilize a moving window to sample multiple patches of a given image leading to a majority decision by the patches for image class assignment. The curvelet-based feature extraction may capture both textural and, implicitly, structural information in an image patch. A tree-structured classifier consisting of three Gaussian-kernel support vector machines each with an embedded voting mechanism has been successfully trained and tested yielding high accuracy to classify tissue images of four critical Gleason scores (GS) 3+3, 3+4, 4+3 and 4+4. The experimental result has demonstrated an enhanced performance as compared to other reported works.