In this paper, a downlink intelligent reflecting surface (IRS) enhanced millimeter-wave (mmWave) non-orthogonal multiple access (NOMA) system is considered. A joint optimization problem over active beamforming, passive beamforming and power allocation is formulated. Due to the highly coupled variables, the formulated optimization problem is non-convex. To solve this problem, an alternative optimization and successive convex approximation based iterative algorithm is proposed. Numerical results illustrate that: 1) the proposed scheme offers significant sum-rate gains, which confirms the effectiveness of introducing IRS for mmWave-NOMA systems; 2) the proposed algorithm with discrete phase shifts can achieve close performance to that of continuous phase shifts.