This paper considers a cellular two-way relay network with one base station (BS), one relay station (RS), and two users. The two users are far from the BS and no direct links exist, and the two users exchange messages with the BS via the RS. A non-orthogonal multiple access (NOMA) and network coding (NC)-based decode-and-forward (DF) two-way relaying (TWR) scheme TWR-NOMA-NC is proposed, which is able to reduce the number of channel-uses to three from four in conventional time-division multiple access (TDMA) based TWR approaches. The achievable sum-rate performance of the proposed approach is analyzed, and a closed-form expression for the sum-rate upper bound is derived. Numerical results show that the analytical sum-rate upper bound is tight, and the proposed TWR-NOMA-NC scheme significantly outperforms the TDMA-based TWR and NOMA-based one-way relaying counterparts.