Title: Demonstration Actor Critic. Abstract: We study the problem of \textit{Reinforcement learning from demonstrations (RLfD)}, where the learner is provided with both some expert demonstrations and reinforcement signals from the environment. One approach leverages demonstration data in a supervised manner, which is simple and direct, but can only provide supervision signal over those states seen in the demonstrations. Another approach uses demonstration data for reward shaping. By contrast, the latter approach can provide guidance on how to take actions, even for those states are not seen in the demonstrations. But existing algorithms in the latter one adopt shaping reward which is not directly dependent on current policy, limiting the algorithms to treat demonstrated states the same as other states, failing to directly exploit supervision signal in demonstration data. In this paper, we propose a novel objective function with policy-dependent shaping reward, so as to get the best of both worlds. We present a convergence proof for policy iteration of the proposed objective, under the tabular setting. Then we develop a new practical algorithm, termed as Demonstration Actor Critic (DAC). Experiments on a range of popular benchmark sparse-reward tasks shows that our DAC method obtains a significant performance gain over five strong and off-the-shelf baselines.