With the continuous improvement of smart oceans, marine networks become more intelligent and efficient in monitoring marine environments and marine resources. However, the limited communication resources (such as bandwidth, battery capacity, etc.) of marine wireless devices have become the major bottleneck problems of marine networks. Additionally, the rationality of marine communication devices lead to the fact that they are not to perform tasks voluntarily. To address these issues, in this paper, we investigate a contract incentive scheme for non-orthogonal multiple access (NOMA) enabled delay minimization for marine multi-access edge computing (MEC) networks. Specifically, we formulate the utility optimization problems for unmanned surface vessels (USVs) and unmanned aerial vehicles (UAVs), respectively. To solve the optimization problems, we propose innovative algorithms which can maximize the utility of each party. We conduct simulation results to verify the performance of the algorithms, and the result shows its efficiency and effectiveness.