In this paper, energy efficient power allocation is considered for a multiuser uplink non-orthogonal multiple access (NOMA) system under quality of service (QoS) constraints. Due to the QoS requirements, the considered energy-efficiency (EE) maximization problem may be infeasible and it is first required to determine the feasibility conditions. Then in a feasible region, the considered problem is shown to be pseudo-concave and can be solved by employing Dinkelbach's algorithm. Moreover, for the two extreme cases with very low and high maximum transmit power constraints, analytical results are provided, which shed light on how power is allocated to each user to maximize the EE. Simulation results are presented, which show that with a low maximum transmit power constraint, NOMA may perform worse than the conventional orthogonal multiple access (OMA) in terms of EE. However, under a high maximum transmit power constraint, NOMA always outperforms OMA.