The study of gene regulatory network (GRN) and protein protein interaction network (PPI) is believed to be fundamental to the understanding of molecular processes and functions in system biology and therefore, attracted more and more attentions in past few years. However, there is little focus about network construction in single nucleotide polymorphism (SNP) level, which may provide a direct insight into mutations among individuals, potentially leading to new pathogenesis discovery and diagnostics. In this paper, we present a novel method to mine, model and evaluate a SNP sub-network from SNP-SNP interactions. Specifically, based on logistic regression between two SNPs, we first construct a genome-wide SNP-SNP interaction network. Then by using gene information, selected SNP seeds are employed to detect SNP sub-networks with a maximal modularity. Finally to identify functional role of each SNP sub-network, its gene association network is constructed and their functional similarity values are calculated to show the biological relevance. Results show that our method is effective in SNP sub-network extraction and gene function prediction.