Bayesian Predictive Coding (BPC) is a Bayesian extension to the influential theory of Predictive Coding (PC) in information processing in the brain.BPC estimates a posterior distribution over network parameters, allowing for better quantification of epistemic uncertainty.Compared to PC, BPC converges in fewer epochs in the full-batch setting and remains competitive in the mini-batch setting.BPC provides a biologically plausible method for Bayesian learning in the brain and offers attractive uncertainty quantification in deep learning.