Integration of methods based on satellite remote sensing into current maritime monitoring strategies could help tackle the problem of global overfishing. Operational software is now available to perform vessel detection on satellite imagery, but research on vessel classification has mainly focused on bulk carriers, container ships, and oil tankers, using high-resolution commercial Synthetic Aperture Radar (SAR) imagery. Here, we present a method based on Random Forest (RF) to distinguish fishing and non-fishing vessels, and apply it to an area in the North Sea. The RF classifier takes as input the vessel’s length, longitude, and latitude, its distance to the nearest shore, and the time of the measurement (am or pm). The classifier is trained and tested on data from the Automatic Identification System (AIS). The overall classification accuracy is 91%, but the precision for the fishing class is only 58% because of specific regions in the study area where activities of fishing and non-fishing vessels overlap. We then apply the classifier to a collection of vessel detections obtained by applying the Search for Unidentified Maritime Objects (SUMO) vessel detector to the 2017 Sentinel-1 SAR images of the North Sea. The trend in our monthly fishing-vessel count agrees with data from Global Fishing Watch on fishing-vessel presence. These initial results suggest that our approach could help monitor intensification or reduction of fishing activity, which is critical in the context of the global overfishing problem.