In wireless heterogeneous networks (HetNets), rational relay node (RN) placement can not only expand network coverage and capacity, but also significantly reduce energy consumption of the network. However, existing RN placement schemes mainly focus on improving network performance, and do not take the network energy consumption and capacity constraints of RNs into consideration, which makes their solutions impractical. Therefore, in this paper, we investigate energy-efficient RN placement (EERPL) problem, and try to reduce energy consumption of a wireless HetNet within the range of RN’s capacity constraints. More specifically, we first present a fine-grained energy consumption model and formulate the EERPL problem, which can be translated to the degree constrained minimum Steiner tree problem. Then, we propose a heuristic RN-placement algorithm HBAPS, which involves two steps, i.e., generating an initial minimum-energy RN placement solution and adjusting the solution to be with in the capacity constraints. Finally, extensive simulations are conducted in both randomly generated scenarios and real trace-based scenarios. Experimental results demonstrate that HBAPS achieves nearly optimal results when the scenario is small, and even in a large scenario, the proposed algorithm still obtains proper solutions within the acceptable time, and outperforms the other two existing heuristic algorithms.