Mining big data in brain imaging genetics is an emerging topic in brain science. It can uncover meaningful associations between genetic variations and brain structures and functions. Sparse canonical correlation analysis (SCCA) is introduced to discover bi-multivariate correlations with feature selection. However, these SCCA methods cannot be directly applied to big brain imaging genetics data due to two limitations. First, they have cubic complexity in the size of the matrix involved and are computational and memory intensive when the matrix becomes large. Second, the parameters in an SCCA method need to be fine-tuned in advance. This further dramatically increases the computational time, and gets severe in high-dimensional scenarios. In this paper, we propose two fast and efficient algorithms to speed up the structure-aware SCCA (S2CCA) implementations without modification to the original SCCA models. The fast algorithms employ a divide-and-conquer strategy and are easy to implement. The experimental results, compared with conventional algorithms, show that our algorithms reduce the time usage significantly. Specifically, the fast algorithms improve the computational efficiency by tens to hundreds of times compared to conventional algorithms. Besides, our algorithms yield similar correlation coefficients and canonical loading profiles to the conventional implementations. Our fast algorithms can be easily parallelized to further reduce the computational time. This indicates that the proposed fast scalable SCCA algorithms can be a powerful tool for big data analysis in brain imaging genetics.