Accurate identification of coherent transcriptional modules (subnetworks) in adipose and muscle tissues is important for revealing the related mechanisms and co-regulated pathways involved in the development of aging-related diseases. Here, we proposed a systematically computational approach, called ICEGM, to Identify the Co-Expression Gene Modules through a novel mathematical framework of Higher-Order Generalized Singular Value Decomposition (HO-GSVD). ICEGM was applied on the adipose, and heart and skeletal muscle tissues in old and young female African green vervet monkeys. The genes associated with the development of inflammation, cardiovascular and skeletal disorder diseases, and cancer were revealed by the ICEGM. Meanwhile, genes in the ICEGM modules were also enriched in the adipocytes, smooth muscle cells, cardiac myocytes, and immune cells. Comprehensive disease annotation and canonical pathway analysis indicated that immune cells, adipocytes, cardiomyocytes, and smooth muscle cells played a synergistic role in cardiac and physical functions in the aged monkeys by regulation of the biological processes associated with metabolism, inflammation, and atherosclerosis. In conclusion, the ICEGM provides an efficiently systematic framework for decoding the co-expression gene modules in multiple tissues. Analysis of genes in the ICEGM module yielded important insights on the cooperative role of multiple tissues in the development of diseases.