Image segmentation is a fundamental problem in biomedical image analysis. Recent advances in deep learning have achieved promising results on many biomedical image segmentation benchmarks. However, due to large variations in biomedical images (different modalities, image settings, objects, noise, etc), to utilize deep learning on a new application, it usually needs a new set of training data. This can incur a great deal of annotation effort and cost, because only biomedical experts can annotate effectively, and often there are too many instances in images (e.g., cells) to annotate. In this paper, we aim to address the following question: With limited effort (e.g., time) for annotation, what instances should be annotated in order to attain the best performance? We present a deep active learning framework that combines fully convolutional network (FCN) and active learning to significantly reduce annotation effort by making judicious suggestions on the most effective annotation areas. We utilize uncertainty and similarity information provided by FCN and formulate a generalized version of the maximum set cover problem to determine the most representative and uncertain areas for annotation. Extensive experiments using the 2015 MICCAI Gland Challenge dataset and a lymph node ultrasound image segmentation dataset show that, using annotation suggestions by our method, state-of-the-art segmentation performance can be achieved by using only 50% of training data.