A Non-Orthogonal Multiple Access （NOMA） based computation offloading and bandwidth allocation strategy was presented to address the issues of insufficient computing capacity of mobile devices and limited spectrum resource in 5G ultra-dense network. Firstly， the system model was analyzed， on this basis， the research problem was defined formally with the objective of minimizing the computation cost of devices. Then， this problem was decomposed into three sub-problems： device computation offloading， system bandwidth allocation， and device grouping and matching， which were solved by adopting simulated annealing， interior point method， and greedy algorithm. Finally， a joint optimization algorithm was used to alternately solve the above sub-problems， and the optimal computation offloading and bandwidth allocation strategy was obtained. Simulation results show that， the proposed joint optimization strategy is superior to the traditional Orthogonal Multiple Access （OMA）， and can achieve lower device computation cost compared to NOMA technology with average bandwidth allocation.