Exact determination of gene network is required to discover the higher-order structures of an organism and to interpret its behavior. Most research work in learning gene networks either assumes that there is no time delay in gene expression or that there is a constant time delay. The paper shows how Bayesian Networks can be applied to represent multi-time delay relationships as well as directed loops. The intractability of the network learning algorithm is handled by using an improved mutual information criteria. Also, a new structure learning algorithm, "Learning By Modification", is proposed to learn the sparse structure of a gene network. The experimental results on synthetic data and real data show that our method is more accurate in determining the gene structure as compared to the traditional methods. Even for transcriptional loops spanning over the whole cell, our algorithm can detect them.