The electrophoresis of a charged colloid particle embedded in a charged hydrogel medium is studied based on the numerical computation of Stokes-Nernst-Planck-Poisson equations. In this study, no prior assumption on surface charge density of the particle, Debye length and imposed external electric field are made. We have compared our computed results for a lower range of surface charge density with the existing analytical solution based on the weakly charged particle and found them in good agreement when the fixed charge density of the hydrogel is low. Nonlinearity effects in gel electrophoresis is pronounced for a thick Debye length and higher values of particle zeta-potential. Even in the absence of a gel medium (free-solution), the numerical procedure used in this work yields mobilities different from the previous theoretical analysis based on the Debye-Hfickel approximation when the scaled zeta-potential exceeds 2 and the Debye length is in the order of the particle size. The strong background electroosmotic flow (EOF) for a high fixed charge density of the polyelectrolyte hydrogel with a mesh size comparable to the particle radius drags the particle along the direction of the EOF. In this case, the electrophoretic velocity of the particle varies with its size. The particle electrophoretic velocity and forces are determined for a wide range of intrinsic parameters values. (C) 2015 Elsevier Ltd. All rights reserved.