In this article, mixing in the combined electroosmotic/pressure driven flows of non-Newtonian fluid in a microchannel with rectangular obstacles and non-homogeneous ζ-potential has been studied numerically. The non-Newtonian behavior of the fluid is considered for the flow field using power law rule. Also, the nonlinear Poisson-Boltzmann equation is used to model the distribution of ions across the channel and the electric potential. Numerical solutions of coupled equations of momentum, electric field and concentration field are performed by means of finite element method. In this study, the effects of various parameters such as pressure gradient, rheological behavior of the fluid and the geometrical and physical parameters of obstacles on the mixing quality are investigated. The results indicate that applying adverse pressure gradient to the flow, the dilatant behavior of the fluid, as well as the height of barriers, are highly effective in the enhancement of the mixing quality within the microchannel. It is found that for microchannels with heterogeneous ζ-potential, increasing the length of obstacles significantly increases the mixing efficiency while for the microchannels with homogeneous ζ-potential, barrier length has a slight effect on mixing efficiency.