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Many machine learning techniques have been used to construct gene regulatory networks (GRNs) through precision matrix that considers conditional independence among genes, and finally produces sparse version of GRNs. This construction can be improved using the auxiliary information like gene expression profile of the related species or gene markers. To reach out this goal, we apply a generalized linear model (GLM) in first step and later a penalized maximum likelihood to construct the gene regulatory network using Glasso technique for the residuals of a multi-level multivariate GLM among the gene expressions of one species as a multi-levels response variable and the gene expression of related species as a multivariate covariates. By considering the intrinsic property of the gene data which the number of variables is much greater than the number of available samples, a bootstrap version of multi-response multivariate GLM is used. To find most appropriate related species, a cross-validation technique has been used to compute the minimum square error of the fitted GLM under different regularization. The penalized maximum likelihood under a lasso or elastic net penalty is applied on the residual of fitted GLM to find the sparse precision matrix. Finally, we show that the presented algorithm which is a combination of fitted GLM and applying the penalized maximum likelihood on the residual of the model is extremely fast, and can exploit sparsity in the constructed GRNs. Also, we exhibit flexibility of the proposed method presented in this paper by comparing with the other methods to demonstrate the super validity of our approach.