Electrophoresis is one of the most widely used analytical tools for the quantification of the charged conditions on the surface of fine particles including biological entities. Although it has been studied extensively in the past, relevant results for the case when the dispersion medium is non-Newtonian are very limited. This may occur, for example, when the concentration of the dispersed phase is not low, which is not uncommon in practice. Here, the electrophoresis of a concentrated spherical dispersion in a Carreau. fluid is analyzed theoretically under the conditions of low electric potential and weak external applied electrical field. A pseudospectral method coupled with a Newton-Raphson iteration procedure is used to solve the electrokinetic equations describing the phenomenon under consideration. We conclude that the more significant the shear thinning effect of the fluid, the larger the mobility, and this phenomenon is pronounced for the case when the double layer surrounding a particle is thin. We show that if the double layer is thin and the effect of shear thinning is significant, a second vortex can be observed in the neighborhood of a particle.