To obtain a screening tool for colorectal cancer (CRC) based on gut microbiota, we seek here to identify an optimal classifier for CRC detection as well as a novel nonlinear feature selection method for determining the most discriminative microbial species. In this study, the intestinal micro flora in feces of 141 patients were modeled using general regression neural networks (GRNNs) combined with the proposed feature selection method. The proposed model led to slightly higher accuracy (AUC=0.911) than previous studies (AUC<0.87). The results show that the Clostridium scindens and Bifid bacterium angulatum are indicators of healthy gut flora and CRC happens to reduce these bacterial species. In addition, Fuso bacterium gonidiaformans was found to be closely correlated with the CRC. The occurrence of colorectal adenoma was not sufficiently discriminatory based on fecal microbiota implicating that the change of colonic flora happens in the advanced phase of CRC development rather than initial adenoma. Integrating the proposed model with fecal occult blood test (FOBT), the CRC detection accuracy remained nearly unchanged (AUC=0.915). The performance of proposed method is validated using independent cohorts from America and Austria. Our results suggest that proposed feature selection method combined with GRNN is potentially an accurate method for CRC detection. This project is implemented with MATLAB software.