The electro-osmotic flow of a non-Newtonian fluid in a slit micro-channel under the Navier's slip boundary condition is investigated. The Eyring constitutive relationship model is adopted to describe the non-Newtonian characteristics of the flow driven by the applied electric field force and pressure. In consideration of the micro-scale effects, electric field, non-Newtonian behavior and slip boundary condition, a mechanical model is built and the effects of these factors on the flow are studied. Analytical expressions are derived for the electric potential and velocity profile by solving the linearized Poisson-Boltzmann equation and the modified Cauchy equation. Approximate expressions of the velocity distribution are also given and discussed. Furthermore, by comparing the effects of electric force with that of pressure on the velocity distribution, some meaningful conclusions are drawn from the obtained graphics.