Annotated data samples in real-world applications are often limited. Meta-learning, which utilizes prior knowledge learned from related tasks and generalizes to new tasks of limited supervised experience, is an effective approach for few-shot learning. However, standard meta-learning with globally shared knowledge cannot handle the task heterogeneity problem well, i.e., tasks lie in different distributions. Recent advances have explored several ways to trigger task-dependent initial parameters or metrics, in order to customize task-specific information. These approaches learn task contextual information from data, but ignore external domain knowledge that can help in the learning process. In this paper, we propose a task-adaptive network (TAdaNet) that makes use of a domain-knowledge graph to enrich data representations and provide task-specific customization. Specifically, we learn a task embedding that characterizes task relationships and tailors task-specific parameters, resulting in a task-adaptive metric space for classification. Experimental results on a few-shot image classification problem show the effectiveness of the proposed method. We also apply it on a real-world disease classification problem, and show promising results for clinical decision support.