The control of a predator's locomotion is critical to its ability to capture prey. Flying animals adjust their heading continuously with control similar to guided missiles. However, many animals do not move with rapid continuous motion, but rather interrupt their progress with frequent pauses. To understand how such intermittent locomotion may be controlled during predation, we examined the kinematics of zebrafish (Danio rerio) as they pursued larval prey of the same species. Like many fishes, zebrafish move with discrete burst-and-coast swimming. We found that the change in heading and tail excursion during the burst phase was linearly related to the prey's bearing. These results suggest a strategy, which we call intermittent pure pursuit, that offers advantages in sensing and control. This control strategy is similar to perception and path-planning algorithms required in the design of some autonomous robots and may be common to a diversity of animals.