Predators must frequently balance competing approach and avoidance behaviors elicited by a moving and potentially dangerous prey. Several brain circuits supporting predation have recently been localized. However, the mechanisms by which these circuits balance the conflict between approach and avoidance responses remain unknown. Laboratory mice initially show alternating approach and avoidance responses toward cockroaches, a natural prey, but with repeated exposure become avid hunters. Here we used in vivo neural activity recording and cell-type specific manipulations in hunting mice to identify neurons in the lateral hypothalamus and periaqueductal grey that encode and control predatory approach and avoidance. We found a subset of GABAergic neurons in lateral hypothalamus that specifically encoded hunting behaviors and whose stimulation triggered predation, but not feeding. This population projects to the periaqueductal grey and stimulation of these projections promoted predation. Neurons in periaqueductal grey encoded both approach and avoidance behaviors, but only initially when the mouse showed high levels of fear of the prey. Our findings allow us to propose that GABAergic neurons in lateral hypothalamus facilitate predation in part by suppressing defensive responses to prey encoded in the periaqueductal grey. Our findings reveal a neural circuit mechanism for controlling the balance between conflicting approach and avoidance behaviors elicited by the same stimulus.