We introduce an active learning framework for general sequence learning tasks including sequence labeling and generation. Most existing active learning algorithms mainly rely on an uncertainty measure derived from the probabilistic classifier for query sample selection. However, such approaches suffer from two shortcomings in the context of sequence learning including 1) cold start problem and 2) label sampling dilemma. To overcome these shortcomings, we propose a deep-learning-based active learning framework to directly identify query samples from the perspective of adversarial learning.  Our approach intends to offer labeling  priorities for sequences whose information content are least covered by existing labeled data. We verify our sequence-based active learning approach  on two tasks including sequence labeling and sequence generation.