This paper presents an improved sleep control algorithm for small base stations (SBSs) in 5G New Radio (NR) heterogeneous cellular networks (HetNets). HetNets consist of various base station tiers, including macro base stations (MBSs) and small base stations (SBSs), and have been suggested as a promising solution to enhance wireless coverage and network capacity, employing many SBSs into the MBS coverage. However, power consumption increases significantly as a result of an increase in the number of the SBSs. To solve this problem, the SBS sleep control has been proposed to reduce power consumption for the SBSs and improves energy efficiency, whereas it deteriorates system throughput compared with no sleep control system, consequently degrading the quality of service (QoS) performance at user equipments (UEs). This paper proposes an enhanced algorithm for SBS sleep control based on energy efficiency as a decision criterion for SBS operating state. From the evaluation results through computer simulation, the proposed scheme can provide improved performance for both energy efficiency and system throughput simultaneously, that is it can improve energy efficiency while maintaining almost the same system throughput as the no sleep control system. Concretely, the proposed scheme has the 14.89% improvement in energy efficiency while providing almost the same system throughput of over 99%, compared with no sleep control system.