In this paper, we propose a user selection algorithm for full-duplex cellular system. In full-duplex cellular system, besides self-interference (SI), the user-equipment (UE)-UE interference at downlink (DL) users is induced by adjacent uplink (UL) users thereby degrading the performance severely. Thus, we alleviate the UE-UE interference and improve the achievable rate of UL users at the same time by means of our proposed user selection algorithm. Specifically, we first adopt semiorthogonal user selection (SUS) algorithm [13] with ZF precoder for DL users and then we select UL users considering the trade-off between increasing the rate of UL users and decreasing the UE-UE interference. Moreover, we also propose a mode selection based on our proposed algorithm. As a result, we provide the improved achievable sum-rate of full-duplex system as guaranteeing better achievable rate for both DL and UL users, compared with those of users in half-duplex system. In addition, we analyze the complexity of the proposed user selection algorithm along with analysis of full-search algorithm. In the end, we observe that the numerical results show the improved achievable sum-rate of the proposed user selection algorithm.