Hyperspectral imaging (HSI) is being explored in endoscopy as a tool to extract biochemical information that may improve contrast for early cancer detection in the gastrointestinal tract. Motion artefacts during medical endoscopy have traditionally limited HSI application, however, recent developments in the field have led to real-time HSI deployments. Unfortunately, traditional HSI analysis methods remain unable to rapidly process the volume of hyperspectral data in order to provide real-time feedback to the operator. Here, a convolutional neural network (CNN) is proposed to enable online classification of data obtained during HSI endoscopy. A five-layered CNN was trained and fine-tuned on a dataset of 300 hyperspectral endoscopy images acquired from a planar Macbeth ColorChecker chart and was able to distinguish between its 18 constituent colors with an average accuracy of 94.3% achieved at 8.8 fps. Performance was then tested on a set of images simulating an endoscopy environment, consisting of color charts warped inside a rigid tube mimicking a lumen. The algorithm proved robust to such variations, with classification accuracies over 90% being obtained despite the variations, with an average drop in accuracy of 2.4% being registered at the points of longest working distance and most inclination. For further validation of the color-based classification system, ex vivo videos of a methylene blue dyed pig esophagus and images of different disease stages in the human esophagus were analyzed, showing spatially distinct color classifications. These results suggest that the CNN has potential to provide color-based classification during real-time HSI in endoscopy.