The paper focuses on the online binary problem in imbalanced data stream. Presently, majority existing works rely on a known distribution in advance of the labeled training data, this paper considers a more challenging setting where no prior knowledge is supplied. A second-order online learning method with multiple thresholds based on F-measure is utilized. The F-measure optimization problem provided foundation and inspiration for threshold selection in this paper. The based learner paired with the highest F-score yielding threshold is selected as the optimal classifier for every observed example. Experimentation on recent benchmark datasets validates the superiority of the proposed approach in both balanced and imbalanced data streams.