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Online Action Detection (OAD) in videos is proposed as a per-frame labeling task to address the real-time prediction tasks that can only obtain the previous and current video frames. This paper presents a novel learning-with-privileged based framework for online action detection where the future frames only observable at the training stages are considered as a form of privileged information. Knowledge distillation is employed to transfer the privileged information from the offline teacher to the online student. We note that this setting is different from conventional KD because the difference between the teacher and student models mostly lies in input data rather than the network architecture. We propose Privileged Knowledge Distillation (PKD) which (i) schedules a curriculum learning procedure and (ii) inserts auxiliary nodes to the student model, both for shrinking the information gap and improving learning performance. Compared to other OAD methods that explicitly predict future frames, our approach avoids learning unpredictable unnecessary yet inconsistent visual contents and achieves state-of-the-art accuracy on two popular OAD benchmarks, TVSeries and THUMOS14.