Polyelectrolyte chains grafted to a substrate attain a brush like configuration above a critical grafting density. Polyelectrolyte brushes (PE) have gained significant attention in the last few decades due to a myriad of applications like flow control, biosensing, current rectification, ion manipulation etc. We present a self-consistent model of backbone charged pH-responsive PE brushes using the Strong Stretching Theory (SST). State of the art theoretical model (we refer to it as model 1) for the pH-responsive PE brushes assume a Boltzmann distribution for hydrogen ions both inside and outside the PE layer. In other words, the effect of the coupling between the brush ionization and local hydrogen ion concentration is not considered. This is a major limitation of the existing theory that has been hitherto overlooked. We propose a new theory that self-consistently calculates the correct hydrogen ion distribution by accounting for the appropriate coupling between the brush ionization and local hydrogen ion concentration. We obtain a pair of coupled ordinary differential equations in electrostatic potential and hydrogen ion concentration that are solved numerically to obtain (a) the monomer profile, (b) the distribution of chain ends, (c) the electrostatic potential, and (d) the hydrogen ion distribution. Our results indicate a larger deviation from the results of model 1 at lower bulk salt concentrations and higher pH values. The self-consistent theory always predicts a smaller brush height in comparison to that predicted by model 1. In addition, we observe an enhanced biasness of the monomer concentration profile towards the base than the brush tip.