Dynamic Bayesian inference allows a system to infer the environmental state under conditions of limited sensory observation. Using a goal-reaching task, we found that posterior parietal cortex (PPC) and adjacent posteromedial cortex (PM) implemented the two fundamental features of dynamic Bayesian inference: prediction of hidden states using an internal state transition model and updating the prediction with new sensory evidence. We optically imaged the activity of neurons in mouse PPC and PM layers 2, 3 and 5 in an acoustic virtual-reality system. As mice approached a reward site, anticipatory licking increased even when sound cues were intermittently presented; this was disturbed by PPC silencing. Probabilistic population decoding revealed that neurons in PPC and PM represented goal distances during sound omission (prediction), particularly in PPC layers 3 and 5, and prediction improved with the observation of cue sounds (updating). Our results illustrate how cerebral cortex realizes mental simulation using an action-dependent dynamic model.