We investigate the correspondence between genetic variations with single nucleotide polymorphism (SNP) and brain activity measured by functional magnetic resonance imaging (fMRI). A group sparse canonical correlation analysis method (group sparse CCA) was proposed to explore the correlation between these two types of data, which are high dimensional with small number of samples. It can exploit the group or structural information within the data while filter out irrelevant features within each group. Our method outperforms the existing sparse CCA (sCCA) models in a simulation study. By applying it to the analysis of real data, we identified two pairs of significant canonical variates with correlations 0.7692 and 0.7168 respectively. A gene and brain region of interest (ROI) correlation analysis was further performed on the two pairs of canonical variates to confirm the correlation between genes and the region of interests in the brain.