To efficiently reduce on-grid energy consumption, the admission control algorithm in the hybrid energy powered cellular network (HybE-Net) with base stations (BSs) powered by on-grid energy and solar energy is studied. In HybE-Net, the fluctuation of solar energy harvesting and energy consumption may result in the imbalance of solar energy utilization among BSs, i.e., some BSs may be surplus in solar energy, while others may maintain operation with on-grid energy supply. Obviously, it makes solar energy not completely useable, and on-grid energy cannot be reduced at capacity. Thus, how to control user admission to improve solar energy utilization and to reduce on-grid energy consumption is a great challenge. Motivated by this, we first model the energy flow behavior by using stochastic queue model, and dynamic energy characteristics are analyzed mathematically. Then, fuzzy logic based admission control algorithm is proposed, which comprehensively considers admission judgment parameters, e.g., transmission rate, bandwidth, energy state of BSs. Moreover, the index of solar energy utilization balancing is proposed to improve the balance of energy utilization among different BSs in the proposed algorithm. Finally, simulation results demonstrate that the proposed algorithm performs excellently in improving solar energy utilization and reducing on-grid energy consumption of the HybE-Net.