The combination of Non-orthogonal Multiple Access (NOMA) and Multi-antenna Multi-input Multi-output (MIMO) approach has been considered as an assuring multiple access for fifth generation (5G) technology to improve the system network capacity and the efficiency of the spectrum. In this paper, we investigated a MIMO-NOMA based network code, exclusive-OR (XOR) scheme which applies physical layer network coding (PNC) in two-way relay networks to reduce the transmission time slots. The Quadrature Phase Shift Keying (QPSK) modulation technique is selected to apply to enable the data source transmitting with the carrier wave. In this paper, convolutional codes and the Soft Decision Viterbi algorithm is used to encode and decode the information bits. The coded MIMO-NOMA gives the less bit error rate compared to coded NOMA alone. Moreover, we have analyzed the spectral efficiency and energy efficiency in NOMA and MIMO-NOMA. The sum capacity and transmission rate are also compared in NOMA and MIMO-NOMA scheme. The simulation results show that MIMO-NOMA has higher spectral efficiency and faster transmission rate than NOMA scheme. Finally, the user fairness of MIMO-NOMA has been evaluated.