Accurate preoperative differential diagnosis of fat-poor angiomyolipoma (fp-AML) and clear cell renal cell carcinoma (ccRCC) is essential for proper treatment planning. In this paper, we develop an effective radiomics model for reliable noninvasive discrimination of fp-AML from ccRCC, which incorporates a sophisticated feature selection procedure and a sparse radial basis function neural network (sRBFNN). Specifically, 774 three-dimensional radiomics features are first extracted from contrast-enhanced computed tomography (CECT) images. Pearson’s correlation matrices and Welch’s t-test are used to remove the insignificant features, then sequential forward floating selection method is utilized to select the discriminative features. Finally, the sRBFNN is employed for classification. The radiomics model is examined by leave-one-out cross validation and yields the best performance of 90.00%, 66.67%, 100.0%, and 0.9173 in terms of prediction accuracy, sensitivity, specificity, and the area under the receiver operating characteristic curves, respectively. Furthermore, the reliability of the predictions is verified by evaluating the probabilistic outputs of the sRBFNN. The experimental results demonstrate that the developed radiomics model has great potential in the noninvasive discrimination of fp-AML from ccRCC.