Marine Internet of Things (IoT) systems have grown substantially with the development of nonterrestrial networks (NTNs) via aerial and space vehicles in the upcoming sixth-generation (6G), thereby assisting environment protection, military reconnaissance, and sea transportation. Due to the unpredictable climate changes and the extreme channel conditions of maritime networks, however, it is challenging to efficiently and reliably collect and compute a huge amount of maritime data. In this article, we propose a hybrid low-Earth orbit (LEO) and unmanned aerial vehicle (UAV) edge computing method in space–air–sea integrated networks for marine IoT systems. Specifically, two types of edge servers mounted on UAVs and LEO satellites are endowed with computational capabilities for the real-time utilization of a sizable data collected from ocean IoT sensors. Our system aims at minimizing the total energy consumption of the battery-constrained UAV by jointly optimizing the bit allocation of communication and computation along with the UAV path planning under latency, energy budget, and operational constraints. For availability and practicality, the proposed methods are developed for three different cases according to the accessibility of the LEO satellite, “Always On,” “Always Off,” and “Intermediate Disconnected,” by leveraging successive convex approximation (SCA) strategies. Via numerical results, we verify that significant energy savings can be accrued for all cases of LEO accessibility by means of joint optimization of bit allocation and UAV path planning compared to partial optimization schemes that design for only the bit allocation or trajectory of the UAV.