Abstract: To address the problem of low transmission rate of non-orthogonal multiple access (NOMA) system in wireless environment, we propose an IRS-assisted uplink NOMA and rate maximization algorithm based on the property that intelligent reflecting surface (IRS) can change the phase shift of the incident signal. First, a joint user power and IRS phase shift multivariate optimization model is constructed under the constraints of per-user power, per-user minimum rate, and IRS phase shift. Then, the original nonconvex problem is converted into two easily handled subproblems by equivalent simplification of the problem formulation. Finally, the subproblems are solved by the alternating direction method of multipliers (ADMM) and the introduction of relaxation variables. The simulation results show that the proposed algorithm improves the sum rate of the system by 0.4 bit/(s·Hz) on average compared with the successive convex approximation (SCA), which proves that the ADMM-based algorithm is effective in improving the sum rate of the system.