Smooth pursuit eye movements are important for vision because they maintain the line of sight on targets that move smoothly within the visual field. Smooth pursuit is driven by neural representations of motion, including a surprisingly strong influence of high-level signals representing expected motion. We studied anticipatory smooth eye movements (defined as smooth eye movements in the direction of expected future motion) produced by salient visual cues in a group of high-functioning observers with Autism Spectrum Disorder (ASD), a condition that has been associated with difficulties in either generating predictions, or translating predictions into effective motor commands. Eye movements were recorded while participants pursued the motion of a disc that moved within an outline drawing of an inverted Y-shaped tube. The cue to the motion path was a visual barrier that blocked the untraveled branch (right or left) of the tube. ASD participants showed strong anticipatory smooth eye movements whose velocity was the same as that of a group of neurotypical participants. Anticipatory smooth eye movements appeared on the very first cued trial, indicating that trial-by-trial learning was not responsible for the responses. These results are significant because they show that anticipatory capacities are intact in high-functioning ASD in cases where the cue to the motion path is highly salient and unambiguous. Once the ability to generate anticipatory pursuit is demonstrated, the study of the anticipatory responses with a variety of types of cues provides a window into the perceptual or cognitive processes that underlie the interpretation of events in natural environments or social situations.