Of widespread interest in animal behaviour and ecology is how animals search their environment for resources, and whether these search strategies are optimal. However, movement also affects predation risk through effects on encounter rates, the conspicuousness of prey, and the success of attacks. Here we use predatory fish attacking a simulation of virtual prey to test whether predation risk is associated with movement behaviour. Despite often being demonstrated to be a more efficient strategy for finding resources such as food, we find that prey displaying Lévy motion are twice as likely to be targeted by predators than prey utilising Brownian motion. This can be explained by the predators, at the moment of the attack, preferentially targeting prey that were moving with straighter trajectories rather than prey that were turning more. Our results emphasise that costs of predation risk need to be considered alongside the foraging benefits when comparing different movement strategies.