Online multi-object tracking aims at estimating the tracks of multiple objects instantly with each incoming frame and the information provided up to the moment. It still remains a difficult problem in complex scenes, because of the large ambiguity in associating multiple objects in consecutive frames and the low discriminability between objects appearances. In this paper, we propose a robust online multi-object tracking method that can handle these difficulties effectively. We first define the tracklet confidence using the detectability and continuity of a tracklet, and decompose a multi-object tracking problem into small subproblems based on the tracklet confidence. We then solve the online multi-object tracking problem by associating tracklets and detections in different ways according to their confidence values. Based on this strategy, tracklets sequentially grow with online-provided detections, and fragmented tracklets are linked up with others without any iterative and expensive association steps. For more reliable association between tracklets and detections, we also propose a deep appearance learning method to learn a discriminative appearance model from large training datasets, since the conventional appearance learning methods do not provide rich representation that can distinguish multiple objects with large appearance variations. In addition, we combine online transfer learning for improving appearance discriminability by adapting the pre-trained deep model during online tracking. Experiments with challenging public datasets show distinct performance improvement over other state-of-the-arts batch and online tracking methods, and prove the effect and usefulness of the proposed methods for online multi-object tracking.