<p>Current hyperelastic constitutive models of hydrogels face difficulties in capturing the stress-strain behaviors of hydrogels under extremely large deformation because the effect of non-affine deformation of the polymer network inside is ambiguous. In this work, we construct periodic random network (PRN) models for the effective polymer network in hydrogels and investigate the non-affine deformation of polymer chains intrinsically originates from the structural randomness from bottom up. The non-affine deformation in PRN models is manifested as the actual stretch of polymer chains randomly deviated from the chain stretch predicted by affine assumption, and quantified by a non-affine ratio of each polymer chain. It is found that the non-affine ratios of polymer chains are closely related to bulk deformation state, chain orientation, and initial chain elongation. By fitting the non-affine ratio of polymer chains in all PRN models, we propose a non-affine constitutive model for the hydrogel polymer network based on micro-sphere model. The stress-strain curves of the proposed constitutive models under uniaxial tension condition agree with the simulation results of different PRN models of hydrogels very well.</p>