Background/Aims: Brain functional connectivity networks constructed from resting-state functional magnetic resonance imaging (rs-fMRI) have been widely used for classifying Alzheimer's disease (AD) from normal controls (NC). However, conventional correlation analysis methods only capture the pairwise information, which may not be capable of revealing an adequate and accurate functional connectivity relationship among brain regions in the whole brain. Additionally, the non-sparse connectivity networks commonly contain a large number of spurious or insignificant connections, which are inconsistent with the sparse connectivity of actual brain networks in nature and may deteriorate the classification performance of Alzheimer's disease. Methods: To address these problems, in this paper, a new classification framework is proposed by combining the Group-constrained topology structure detection with sparse inverse covariance estimation (SICE) method to build the functional brain sub-network for each brain region. Particularly, to tune the sensitive analysis of the regularized parameters in the SICE method, a nested leave-one-out cross-validation (LOOCV) method is adopted. Sparse functional connectivity networks are thus effectively constructed by using the optimal regularized parameters. Finally, a decision classification tree (DCT) classifier is trained for classifying AD from NC based on these optimal functional brain sub-networks. The convergence performance of our proposed method is furthermore evaluated by the trend of coefficient variation. Results: Experiment results indicate that a LOOCV classification accuracy of 81.82% with a sensitivity of 80.00%, and a specificity of 83.33% can be obtained by using the proposed method for the classification AD from NC, and outperforms the most state-of-the-art methods in terms of the classification accuracy. Additionally, the experiment results of the convergence performance further suggest that our proposed scheme has a high rate of convergence. Particularly, the abnormal brain regions and functional connections identified by our proposed framework are highly associated with the underpinning pathological mechanism of the AD, which are consistent with previous studies. Conclusion: These results have demonstrated the effectiveness of the proposed Group-constrained SICE method, and are capable of clinical value to the diagnosis of Alzheimer's disease.