With the development of marine economy, more marine applications emerge leading to more deployed sensors and more generated data. However, current marine Internet only provides low transmission rate constrained by limited communication resources and bad transmission environment. How to efficiently use these resources and guarantee quality-of-service (QoS) of applications need to be addressed. This paper proposes an online optimization resource management algorithm to improve the communication resource efficiency with guaranteed QoSs for different applications. This algorithm needs neither of the resource cost function nor QoS constraint function at the resource scheduling node. Furthermore, the gradient information, which is usually needed in learning strategies, is not required either. Instead, this algorithm performs resource management of both computation and communication resources in each time slot only based on the observation of the last time slot. With slot-by-slot resource allocation, the communication cost can be minimized to be suitable for maritime scenarios. In the meantime, a long-term delay constraint can be satisfied. Results show that the proposed algorithm achieves the goal of reducing communication cost while guaranteeing the delay-constraint of different applications. Although more computation resources will improve its performance, this algorithm still can obtain the minimized cost given a low computation resource. INDEX TERMS Online resource management, data feedback, edge computing, maritime communications.