Conversational video question answering is a challenging task in visual information retrieval, which generates the accurate answer from the referenced video contents according to the visual conversation context and given question. However, the existing visual question answering methods mainly tackle the problem of single-turn video question answering, which may be ineffectively applied for multi-turn video question answering directly, due to the insufficiency of modeling the sequential conversation context. In this paper, we study the problem of multi-turn video question answering from the viewpoint of multi-step hierarchical attention context network learning. We first propose the hierarchical attention context network for context-aware question understanding by modeling the hierarchically sequential conversation context structure. We then develop the multi-stream spatio-temporal attention network for learning the joint representation of the dynamic video contents and context-aware question embedding. We next devise the hierarchical attention context network learning method with multi-step reasoning process for multi-turn video question answering. We construct two large-scale multi-turn video question answering datasets. The extensive experiments show the effectiveness of our method.