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This paper investigates a challenging task named peptide sequencing which aims to generate a peptide sequence based on a given mass spectrum. Peptide sequencing is a critical task for protein quantitative analysis and mechanism research. Towards that end, we propose a novel approach for peptide sequence generation based on a general reinforcement learning framework. Specifically, we formulate the peptide sequence generation as a multi-step decision-making process which is optimized with a reward function. To encourage producing accuracy sequences, we train a policy function that determines the next amnio acid according to current state and a value function which estimates all possible extensions of current policy through an actor-critic strategy. Experiments on a wide variety of public data sets show that our proposed model outperforms previous state-of-the-art methods, achieving a higher precision at the spectrum level.