Deep neural networks have been extensively studied for undersampled MRI reconstruction. While achieving state-of-the-art performance, they are trained and deployed specifically for one anatomy with limited generalization ability to another anatomy. Rather than building multiple models, a universal model that reconstructs images across different anatomies is highly desirable for efficient deployment and better generalization. Simply mixing images from multiple anatomies for training a single network does not lead to an ideal universal model due to the statistical shift among datasets of various anatomies, the need to retrain from scratch on all datasets with the addition of a new dataset, and the difficulty in dealing with imbalanced sampling when the new dataset is further of a smaller size. In this paper, for the first time, we propose a framework to learn a universal deep neural network for undersampled MRI reconstruction. Specifically, anatomy-specific instance normalization is proposed to compensate for statistical shift and allow easy generalization to new datasets. Moreover, the universal model is trained by distilling knowledge from available independent models to further exploit representations across anatomies. Experimental results show the proposed universal model can reconstruct both brain and knee images with high image quality. Also, it is easy to adapt the trained model to new datasets of smaller size, i.e., abdomen, cardiac and prostate, with little effort and superior performance.