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Automatic surgical workflow recognition in video is an essentially fundamental yet challenging problem for developing computer-assisted and robotic-assisted surgery. Existing approaches with deep learning have achieved remarkable performance on analysis of surgical videos, however, heavily relying on large-scale labelled datasets. Unfortunately, the annotation is not often available in abundance, because it requires the domain knowledge of surgeons. In this paper, we propose a novel active learning method for cost-effective surgical video analysis. Specifically, we propose a non-local recurrent convolutional network (NL-RCNet), which introduces non-local block to capture the long-range temporal dependency (LRTD) among continuous frames. We then formulate an intra-clip dependency score to represent the overall dependency within this clip. By ranking scores among clips in unlabelled data pool, we select the clips with weak dependencies to annotate, which indicates the most informative ones to better benefit network training. We validate our approach on a large surgical video dataset (Cholec80) by performing surgical workflow recognition task. By using our LRTD based selection strategy, we can outperform other state-of-the-art active learning methods. Using only up to 50% of samples, our approach can exceed the performance of full-data training.