Marine debris pollution is increasingly threatening the marine environment and human health. The most effective way to remove macro-debris floating offshore is to send vessels to collect it. We employ advanced remote sensing technology to locate debris and vessels equipped with a hybrid energy system composed of photovoltaic, battery packs and diesel to collect debris. In order to establish an effective collection mechanism in an economical and eco-friendly manner, we propose a two-stage optimization approach of vessel routing and energy management strategy. In the first stage, a mixed integer linear programming is to minimize the vessel travel time for removing debris, which is reduced to the vessel routing problem with time window considering discrete speed. Advanced remote sensing technology and trajectory prediction software are used to locate debris at sea. An adaptive large neighborhood search algorithm with pheromone heuristic rule is tailored to solve the problem. A mixed integer linear programming model is proposed to optimize the power flow for the hybrid energy system in the second stage. The objective is to minimize the total cost, taking into account of the constraints of power load balance, battery charge and discharge state and output limit of each energy source. The proposed models and algorithm are validated by a group of numerical examples with different sizes. Compared with VRP Spreadsheet Solver and CPLEX solver, our proposed algorithm not only has obvious advantages in both time and results, but also has cubic function fitting property in time complexity within 100 data. We also compare the optimal power flow and total cost under three illumination intensity scenarios and analyze the optimal power flow for each energy. We find that in optimal power flow, diesel can charge the battery only if it supplies power to vessel load. The results show that compared with the pure diesel system, the hybrid energy system has an overwhelming advantage in terms of total cost and carbon emissions, which can be reduced by 65.78% and 82.69%, respectively. We also find no change in the cost savings of hybrid vessels when considering battery and diesel life-cycle carbon emissions.