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Biomedical sensor networks have been widely used in medical applications, where data packets usually contain vital sign information and the network used for communications should guarantee that these packets can be delivered to the medical center reliably and efficiently. In other words, a set of requirements for quality of services (QoS) must be satisfied. In this paper, RL-QRP, a reinforcement learning based routing protocol with QoS-support is proposed for biomedical sensor networks. In RL-QRP, optimal routing policies can be found through experiences and rewards without the need of maintaining precise network state information. Simulation results show that RL-QRP performs well in terms of a number of QoS metrics and energy efficiency in various medical scenarios. By investigating the impacts of network traffic load and sensor node mobility on the network performance, RL-QRP has been proved to fit well in dynamic environments.