Task-switching is a fundamental cognitive ability that allows animals to update their knowledge of current rules or contexts. Detecting discrepancies between predicted and observed events is essential for this process. However, little is known about how the brain computes cognitive prediction-errors and whether neural prediction-error signals are causally related to task-switching behaviours. Here we trained mice to use a prediction-error to switch, in a single trial, between responding to the same stimuli using two distinct rules. Optogenetic silencing and un-silencing, together with widefield and two-photon calcium imaging revealed that the anterior cingulate cortex (ACC) was specifically required for this rapid task-switching, but only when it exhibited neural prediction-error signals. These prediction-error signals were projection-target dependent and were larger preceding successful behavioural transitions. An all-optical approach revealed a disinhibitory interneuron circuit required for successful prediction-error computation. These results reveal a circuit mechanism for computing prediction-errors and transitioning between distinct cognitive states.