Large amount of research efforts have been focused on estimating gene networks based on gene expression data to understand the functional basis of a living organism. Such networks are often obtained by considering pairwise correlations between genes, thus may not reflect the true connectivity between genes. By treating gene expressions as quantitative traits while considering genetic markers, genetical genomics analysis has shown its power in enhancing the understanding of gene regulations. Previous works have shown the improved performance on estimating the undirected network graphical structure by incorporating genetic markers as covariates. Knowing that gene expressions are often due to directed regulations, it is more meaningful to estimate the directed graphical network.