In this paper, a downlink multi-user communication of an intelligent reflecting surface (IRS)-assisted multiple-input single-output (MISO) power-domain non-orthogonal multiple access (NOMA) system is investigated. Considering multi-carrier (MC) transmission and to enhance user fairness, two users are assigned to the same subcarrier. For such a system, the authors optimize active beamforming at the base station (BS), subcarrier allocation policy, and phase shifts at the IRS to maximize the system throughput. A semi-definite relaxation (SDR) is applied to tackle the non-convex optimization problem, and an alternating optimization (AO) algorithm is proposed to obtain a suboptimal solution. Numerical results illustrate the higher throughput of the proposed MC multi-user IRS-aided MISO-NOMA system as compared to the conventional IRS-assisted orthogonal multiple access (OMA) system.