Learning the structures of large undirected graphs with thousands of nodes from data has been an open challenge. In this paper, we use graphical Gaussian model (GGM) as the underlying model and propose a novel ARD style Wishart prior for the precision matrix of the GGM, which encodes the graph structure we want to learn. With this prior, we can get the MAP estimation of the precision matrix by solving (a modified version of) Lasso regressions and achieve a sparse solution. We use our approach to learn genetic regulatory networks from genome-wide expression microarray data and protein-binding location analysis data. Evaluated on the basis of consistency with the GO annotations, the experiments show that our approach has a much better performance than the clustering-based approaches and BN learning approaches in discovering gene regulatory modules.