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Marine debris pollution is becoming an increasingly serious problem, affecting not only navigational safety but also the health of marine ecosystems. Carbon emission causes ocean acidification, which greatly harms marine lives. In order to respond to these environmental issues, this paper studies marine debris collection with consideration of carbon cap using logistics network. To the most of our knowledge, this is first work to study marine debris removal from logistics way. We proposed a three-phase marine debris collection framework: (1) identifying initial locations of the debris; (2) utilizing GNOME software to predict the drifting trajectory of the debris; and (3) formulating vessel routing as a mixed integer nonlinear programming with consideration of carbon emission. The model seeks to minimize the total costs including fuel cost, berth cost, unloading cost in the harbor, vessel rent, vessel insurance, and labor cost, with respect to the constraints of carbon cap, vessel capacities, and time windows. After the linearization process, a Branch-and-Cut (B&C) algorithm with multiple variable fixing techniques and valid inequalities is used to solve the proposed model. The debris dispersion located in Boston vicinity is used as a case study to validate the proposed model and algorithm. The results reveal that the farther away the debris location is from the shore, the higher the collection cost and the more the carbon emission would be. The daily collection cost in the closest location and in the farthest location is $140 lower and $210 higher than that in the initial location. The carbon emission in the farthest location is 21% and 32% higher than that in the initial location and in the closest location. Sensitivity analysis is also carried out for the fuel price and carbon cap to test their impact on total costs These results show that proposed model and algorithm can significantly improve the efficiency of marine debris collection process, reduce carbon emission and total costs. • A three-phase structured framework for marine debris cleanup is firstly proposed. • Vessel velocity has been used as a variable to trade off carbon emission and cost. • A mixed integer nonlinear programming vessel routing problem is firstly formulated. • Α Branch-and-Cut algorithm combined with linearization is used to solve the model. • The vicinity of Boston case study is used to validate the model and algorithm. [ABSTRACT FROM AUTHOR]