Body Area Networks (BANs) consist of various sensors which gather patient's vital signs and deliver them to doctors. One of the most significant challenges faced, is the design of an energy-efficient next hop selection algorithm to satisfy Quality of Service (QoS) requirements for different healthcare applications. In this paper, a novel efficient next hop selection algorithm is proposed in multi-hop BANs. This algorithm uses the minimum hop count and a link cost function jointly in each node to choose the best next hop node. The link cost function includes the residual energy, free buffer size, and the link reliability of the neighboring nodes, which is used to balance the energy consumption and to satisfy QoS requirements in terms of end to end delay and reliability. Extensive simulation experiments were performed to evaluate the efficiency of the proposed algorithm using the NS-2 simulator. Simulation results show that our proposed algorithm provides significant improvement in terms of energy consumption, number of packets forwarded, end to end delay and packet delivery ratio compared to the existing routing protocol.