Brain functional connectivity analysis on fMRI data could improve the understanding of human brain function. However, due to the influence of the inter-subject variability and the heterogeneity across subjects, previous methods of functional connectivity analysis are often insufficient in capturing disease-related representation so that decreasing disease diagnosis performance. In this paper, we first propose a new multi-graph fusion framework to fine-tune the original representation derived from Pearson correlation analysis, and then employ L1-SVM on fine-tuned representations to conduct joint brain region selection and disease diagnosis for avoiding the issue of the curse of dimensionality on high-dimensional data. The multi-graph fusion framework automatically learns the connectivity number for every node (i.e., brain region) and integrates all subjects in a unified framework to output homogenous and discriminative representations of all subjects. Experimental results on two real data sets, i.e., fronto-temporal dementia (FTD) and obsessive-compulsive disorder (OCD), verified the effectiveness of our proposed framework, compared to state-of-the-art methods.