Greening information and communications technology is becoming an environmental and economic sine qua non, and has attracted much research attention. For a cellular network, base stations (BSs) incur more than 50% of the energy consumption of the whole network. Therefore, BSs can be powered by green energy to reduce its on-grid power consumption. Meanwhile, the throughput has always been a critical issue in cellular networks. Since the throughput and energy consumption mutually affect each other, saving on-grid power is at the cost of sacrificing a certain amount of throughput. In this paper, we propose a Throughput Aware and Green Energy aware user association (TAGE) scheme in heterogeneous cellular networks (HCNs) to optimize the trade-off between the throughput and on-grid power consumption. Meanwhile, we employ an energy-throughput coefficient α to control the energy-throughput tradeoff. The simulation results verify that TAGE improves the effective throughput and saves a significant amount of on-grid power for HCNs.