Green communications has received much attention in recent years. In cellular networks, base stations (BSs) account for more than 50 percent of the energy consumption. Reducing energy consumption of BSs is essential to realizing green cellular networks. Utilizing green energy to power BSs is a promising way to reduce the on-grid energy consumption. Maximizing the utilization of green energy has thus been proposed to furthest save the on-grid energy. In this paper, we propose a green energy driven user-BS association with dual battery system to maximize the utilization of green energy at BSs. The BSs of cellular networks are powered by both on-grid energy and green energy. The optimal usage of green energy is achieved by balancing the mobile users among BSs according to the amount of residual green energy in their batteries. This green energy driven user association optimization problem is NP-hard. Hence, we propose some heuristics to maximize the green energy utilization and approximate the optimal user association with low computational complexity. Finally, we validate the performance of the proposed algorithm through extensive simulations.