Cortical computation arises from the interaction of multiple neuronal types, including pyramidal (Pyr) cells and interneurons expressing Sst, Vip, or Pvalb. To study the circuit underlying such interactions, we imaged these four types of cells in mouse primary visual cortex (V1). Our recordings in darkness were consistent with a "disinhibitory" model in which locomotion activates Vip cells, thus inhibiting Sst cells and disinhibiting Pyr cells. However, the disinhibitory model failed when visual stimuli were present: locomotion increased Sst cell responses to large stimuli and Vip cell responses to small stimuli. A recurrent network model successfully predicted each cell type's activity from the measured activity of other types. Capturing the effects of locomotion, however, required allowing it to increase feedforward synaptic weights and modulate recurrent weights. This network model summarizes interneuron interactions and suggests that locomotion may alter cortical computation by changing effective synaptic connectivity