Marine litter in port areas has a huge negative environmental impact and poses a risk to vessels. Therefore port authorities are using special vessels for sweeping. Nowadays, these vessels are usually only deployed after complaints on excessive amounts of marine litter. In this paper an innovative routing method is proposed to sweep marine litter in a port area proactively. The routing method is formulated as a mixed-integer programming (MIP) model. In order to test the sweeping model a dynamic model is developed that predicts the locations in the port area where marine litter will accumulate depending on factors like supply, physical dimensions of port compartments and wind directions. To benchmark the performance of the sweeping model simulations are performed comparing the routing method with other more intuitive policies. It is concluded that using the sweeping policy lower litter levels can be achieved at lower costs.