In this paper, we study the issue of fair resource optimization for an unmanned aerial vehicle (UAV)-enabled mobile edge computing (MEC) system with multi-carrier non-orthogonal multiple access (MC-NOMA). A computation efficiency (CE) optimization problem based on the max-min fairness principle under the partial offloading mode is formulated by optimizing the subchannel assignment, the local CPU frequency, and the transmission power jointly. The formulated problem belongs to the non-convex mixed integer nonlinear programming (MINLP), that is NP-hard to find the global optimal solution. Therefore, we design a polynomial-time algorithm based on the big-M reformulation, the penalized sequential convex programming, and the general Dinkelbach’s method, which can choose an arbitrary point as the initial point and eventually converge to a feasible suboptimal solution. The proposed algorithm framework can be also applied to computation offloading only mode. Additionally, we derive the closed-form optimal solution under the local computing only mode. Simulation results validate the convergence performance of the proposed algorithm. Moreover, the proposed partial offloading mode with the CE maximization scheme outperforms that with the computation bits (CB) maximization scheme with respect to CE, and it can achieve higher CE than the benchmark computing modes. Furthermore, the proposed MC-NOMA scheme can attain better CE performance than the conventional OFDMA scheme.