Allele-specific expression quantification from RNA-seq reads provides opportunities to study the control of gene regulatory networks by cis-acting and trans-acting genetic variants. Many existing methods performed a single-gene and single-SNP association analysis to identify expression quantitative trait loci (eQTLs), and placed the eQTLs against known gene networks for functional interpretation. Instead, we view eQTL data as a capture of the effects of perturbation of gene regulatory system by a large number of genetic variants and reconstruct a gene network perturbed by eQTLs. We introduce a statistical framework called CiTruss for simultaneously learning a gene network and cis-acting and trans-acting eQTLs that perturb this network, given population allele-specific expression and SNP data. CiTruss uses a multi-level conditional Gaussian graphical model to model trans-acting eQTLs perturbing the expression of both alleles in gene network at the top level and cis-acting eQTLs perturbing the expression of each allele at the bottom level. We derive a transformation of this model that allows efficient learning for large-scale human data. Our analysis of the GTEx and LG×SM advanced intercross line mouse data for multiple tissue types with CiTruss provides new insights into genetics of gene regulation. CiTruss revealed that gene networks consist of local subnetworks over proximally located genes and global subnetworks over genes scattered across genome, and that several aspects of gene regulation by eQTLs such as the impact of genetic diversity, pleiotropy, tissue-specific gene regulation, and local and long-range linkage disequilibrium among eQTLs can be explained through these local and global subnetworks.