The friction between two chemically cross-linked polyelectrolyte gels carrying the same sign of charges has been investigated in pure water as well as in salt solutions using a rheometer. It is found that the friction was largely dependent on the charge densities of the gel surface and the ionic strength of the aqueous solution. The chemical structures of the polyelectrolyte gels also play an important role. The friction is described in terms of the hydrodynamic lubrication of the solvent layer between the two gel surfaces, which is formed due to the electrostatic repulsion of the two gel surfaces. The thickness of the solvent layer has been estimated using the Poisson-Boltzmann equation supposing that the ionic osmotic pressure is balanced by the normal pressure applied on the gel. The friction values have been calculated by considering the shear flow of solvent in gel region using the Debye-Binkman equation. For strongly charged polyelectrolyte gels swollen in pure water, the theoretical analysis shows that the friction coefficient almost has no dependence on the water content of the gel, which well agrees with the experimental observations.