In the search for new technologies to assist the fish industry in the fight against diseases, computer vision is playing an essential role. The ability to automatically detect and inspect fish through a camera lens opens up new opportunities. These include both automating currently manual processes as well as introducing new techniques for handling various diseases. The focus of this thesis is to create an algorithm to detect and track fish in underwater video from a fish farm. Several constraints are added to the conditions of the video to make the goal achievable. The algorithm uses classical computer vision approaches for detection, where a tracker is applied for tracking of the fish in succeeding frames. The algorithm aims to have a high success rate on detections made, while not being concerned with detecting all fish. When tested on a video consisting of 671 frames, the algorithm achieved an average precision of 75 %. Considering the difficulty of the video this is considered to be adequate. There is also a focus on the algorithm being low cost in the context of computational complexity, making it relevant for real-time applications. This is also achieved, where minor optimizations to the algorithm will make it perform in real-time.