The problem to be addressed in this paper is to construct a gene functional similarity network using Gene Ontology (GO) annotation data and gene expression data. GO annotation data include functional information of genes, and they are a reliable source to measure gene functional similarity. However, a significant portion, about 25% and 58%, of the human and Arabidopsis genes have no GO term assigned so far. On the other hand, gene expression data consist of levels of gene activation within a cell at a specific moment for all genes. From gene expression data, a co-expression network can be built and used to infer gene function similarity network for GO unknown genes. However, the predicted network based on the co-expression network contains many false positives. DeepFunNet is a new computational method to construct gene functional similarity network for GO unknown genes by strategically utilizing the gene co-expression network. The principle of DeepFunNet is to induce the network construction to select true functional-similarity-edges by propagating known function of a gene to other genes through the co-expression network. To make the propagation step robust, we use level-wise propagation from (GO) known-to-known, known-to-unknown, and unknown-to-unknown gene pairs. DeepFunNet includes a deep learning model for estimating the gene functional similarity of GO unknown genes from neighboring genes. In several experiments, our deep learning model performed better than existing methods.