Greening information and communications technology is becoming an environmental and economic sine qua non, and has attracted much research attention. For a cellular network, the base stations (BSs) cost 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. In this paper, we propose a greeN Energy Aware user associaTion (NEAT) scheme in the two-Tier green heterogeneous network, that enables a BS depleting of green energy to offload its traffic load to other BSs with excessive green energy. Since the Macro BS (MBS) and Pico BS (PBS) employ different partitions of the licensed spectrum, we also consider the bandwidth allocation and adjust the two spectrum partitions dynamically. However, in the NEAT scheme, achieving the optimal user association in terms of minimizing the on-grid power consumption of BSs, is NP-hard. Therefore, we propose a heuristic NEAT algorithm to approximate the optimal solution with low computational complexity. Finally, the performance and viability of the algorithm are substantiated by simulation results.