In this paper, we consider a full duplexing (FD) wireless cellular network where a central base station (BS) works in the FD mode while the downlink (DL) and uplink (UL) users work in the time division duplexing (TDD) mode. Since this FD system induces the inter-user interference from UL user to DL user, the main challenge for maximizing the system performances is user pairing that makes a pair of DL user and UL user to use the same radio resource simultaneously. We formulate two optimization problems for user pairing to maximize the cell throughput or minimize the outage probability, and then propose two suboptimal user pairing algorithms with low complexity. The first algorithm is designed in a way where the DL user with a better signal quality has a higher priority to choose its UL user for the throughput maximization. On the contrary, the second algorithm gives the DL user with a worse signal quality a higher priority to choose its UL user for the outage minimization. Simulation results show that the FD system using the proposed user pairing algorithms achieves the optimal performances and significantly outperforms the conventional TDD system in terms of the cell throughput and the outage probability.