With the increasing exploration of marine resources, various marine wireless devices have been rapidly deployed for different marine applications such as marine navigation, ocean environment monitoring, and seabed resource exploitation. However, due to long transmission delay and low data rate between marine wireless devices and the cloud, it is challenging to satisfy the service requirements of computing-intensive and delay-sensitive tasks. By migrating computing resources from cloud to the near side of ocean, the paradigm of marine edge computing networks, which integrates communication and computation capacities in marine wireless devices, is expected to support a variety of marine tasks (e.g., data collection, monitoring and processing) with low delay and high data rate. However, considering the rationality and selfishness of marine wireless devices and their limited computing-capacity, how to motivate marine wireless devices to conduct task processing becomes an important problem for improving computing efficiency. To address this issue, in this paper, we propose an incentive oriented two-tier task offloading scheme for marine edge computing networks via hybrid Stackelberg-auction game approach, with the objective of improving the offloading efficiency and maximizing marine wireless devices’ utilities. Specifically, for underwater acoustic transmission tier, we exploit multi-access task offloading scheme, in which underwater wireless sensor (UWS) uploads its workloads to an unmanned underwater vehicle (UUV) and a sea surface sink node (SN) via non-orthogonal multiple access (NOMA) transmission. We formulate the utility of each party and model the task offloading process among UWS, UUV and SN as a Stackelberg game to optimize the UWS’s offloading strategy, UUV’s and SN’s price strategies. For radio frequency transmission tier, SN can offload its partial workloads to an unmanned aerial vehicle (UAV) via frequency division multiple access (FDMA) transmission. We provide their utilities and model the offloading process between a SN and a UAV as a double auction game to optimize their bidding strategies. Extensive simulation results are provided to validate the performance of the proposed scheme. Numerical results demonstrate that the proposed algorithms can obtain the optimal solutions and increase the utilities for marine wireless devices.