We investigate the energy-efficient resource allocation problem for the downlink in long-term evolution heterogeneous networks through maximizing the energy efficiency (EE) under the per-user throughput and per-eNB power constraints in this paper. We demonstrate that EE is an increasing function in channel gain, and that EE is continuously differentiable and strictly quasiconcave in transmit power associated with each resource block (RB). Due to the non-convexity of the optimization problem, we develop a two-step resource allocation scheme composed by RB allocation and transmit power control. In the first step, we allocate RBs to users through maximizing the minimum EE of individual user and satisfying the throughput requirement of each user. In the second step, by enforcing the per-user throughput and per-eNB power constraints and exploiting the strict quasiconcavity of EE in transmit power associated with each RB, the power control algorithm is developed to maximize the EE. Simulation results demonstrate the effectiveness of the proposed resource allocation scheme and show that it greatly improves the EE compared with conventional spectral-efficient scheme.