Saccades are ballistic eye movements that rapidly shift gaze from one location of visual space to another. Detecting saccades in eye movement recordings is important not only for studying the neural mechanisms underlying sensory, motor, and cognitive processes, but also as a clinical and diagnostic tool. However, automatically detecting saccades can be difficult, particularly when such saccades are generated in coordination with other tracking eye movements, like smooth pursuits, or when the saccade amplitude is close to eye tracker noise levels, like with microsaccades. In such cases, labeling by human experts is required, but this is a tedious task prone to variability and error. We developed a convolutional neural network (CNN) to automatically detect saccades at human-level performance accuracy. Our algorithm surpasses state of the art according to common performance metrics, and will facilitate studies of neurophysiological processes underlying saccade generation and visual processing.