We consider the electrophoresis of a charged colloid whose surface is assumed to be hydrophobic and whose particle is assumed to be polarizable. The current analysis is based on the numerical solution of the Navier-Stokes-Nernst-Planck-Poisson equations for the nonlinear electrokinetic equations, which are linked with the Laplace equation for the electric field inside the dielectric particle. The particle’s hydrophobicity may affect its electric polarisation by making ions more convectively transportable. The nonlinear effects, such as double-layer polarization and relaxation, are also influenced by the hydrophobicity of the particle surface. A negatively charged colloid is created in the hydrogel medium and translated in the direction of the applied field by the strong electroosmotic flow caused by the hydrogel’s immobile charges. By adjusting the gel’s Debye length and volume charge density, the charged colloid can be trapped.