Methane is an important greenhouse gas, and anthropogenic methane emissions from point sources are a frequent target for emissions reductions. Airborne imaging spectrometers measuring shortwave infrared radiance are becoming regular sources of data for methane point source plume detection and flux estimation. Accurate and efficient detection and delineation of methane plumes will play an essential role in quantifying point source fluxes. Methane plumes are highly variable in space and time, whereas surfaces that are typically “false positive” detections in methane enhancement retrievals are more regularly shaped and change on longer time scales. This work aims to take advantage of plume variability by applying a fully convolutional network (FCN) to detection and delineation of methane plumes within imaging spectrometer time series data. Using a time series of matched filter methane retrieval products derived from Airborne Visible and InfraRed Imaging Spectrometer Next Generation (AVIRIS-NG) data, we demonstrate the ability of a FCN to classify methane plumes at each time step. Comparison with plume detection and delineation using conventional statistical methods demonstrates the value of this approach. Automated approaches incorporating deep learning will become increasingly important as future global satellite missions greatly increase the frequency at which methane point sources are imaged.