Networks models have been widely used in many domains to characterize the interacting relationship between physical entities. A typical problem faced is to identify the networks of multiple related tasks that share some similarities. In this case, a transfer learning approach that can leverage the knowledge gained during the modeling of one task to help better model another task is highly desirable. In this paper, we propose a transfer learning approach, which adopts a Bayesian hierarchical model framework to characterize task relatedness and additionally uses the L₁-regularization to ensure robust learning of the networks with limited sample sizes. A method based on the Expectation-Maximization (EM) algorithm is further developed to learn the networks from data. Simulation studies are performed, which demonstrate the superiority of the proposed transfer learning approach over single task learning that learns the network of each task in isolation. The proposed approach is also applied to identification of brain connectivity networks of Alzheimer's disease (AD) from functional magnetic resonance image (fMRI) data. The findings are consistent with the AD literature.