Many putative Batesian mimics only approximately resemble their supposed models, and such "imperfect" mimics are readily distinguished from defended species by humans and other vertebrates. One explanation for the existence of imperfect mimics is that the most important predators of many mimics have very different sensory and cognitive abilities from those of a typical vertebrate. In such circumstances, selection for more accurate mimicry, as perceived by humans, may be reduced. Little is known, however, about how invertebrate predators perceive and respond to mimicry in insect prey. Here, we investigate the foraging behavior of the crab spider Synema globosum, an important predator of flower-visiting insects at our field site, which frequently encounters both Batesian mimics (hoverflies-Diptera: Syrphidae) and their models (bees and wasps-Hymenoptera). In the field, we found that spiders can distinguish among dipteran and hymenopteran prey taxa, frequently attacking some models and mimics, but avoiding others. Laboratory experiments suggest that some apparently accurate mimic taxa are more likely to be avoided when spiders have prior experience of an aversive wasp model. Avoidance by spiders of black and yellow striped artificial prey suggests visual cues play a role in prey selection, but there was no evidence that olfactory cues are used to identify dangerous or noxious species. Overall, our results provide some support for the hypothesis that invertebrate predator behavior can generate selection on visual signals in putative Batesian mimics.