Enabling nonorthogonal multiple access (NOMA) in device-to-device (D2D) communications under the millimeter wave (mmWave) multiple-input multiple-output (MIMO) cellular network is of critical importance for 5G wireless systems to support low latency, high reliability, and high throughput radio access. In this paper, the closed-form expressions for the outage probability and the ergodic capacity in downlink MIMO-NOMA mmWave cellular network with D2D communications are considered, which indicates that NOMA outperforms TDMA. The influencing factors of performance, such as transmission power and antenna number, are also analyzed. It is found that higher transmission power and more antennas in the base station can decrease the outage probability and enhance the ergodic capacity of NOMA.