To successfully design and operate the micro fluidics system, it is essential to understand the fundamental fluid flow phenomena when channel sizes are shrink to micron or even nano dimensions. One important phenomenon is the electro kinetic effect in micro/nano channels due to the existence of the electrical double layer (EDL) near a solid-liquid interface. Modeling and simulation of electro-kinetic effects on micro flows poses significant numerical challenge due to the fact that the sizes of the double layer (10 nm up to microns) are very "thin" compared to channel width (can be up to 100's of mm). To fully resolve the double layer, tremendous computational cells are required in a typical finite volume method. It is impractical for designing purpose on typical lab-on-chip platform, in which the length of the microchannel can be orders of magnitude greater than the width and the flow geometries are three dimensional and complicated. In this study, a novel sub-grid integration method to properly account for the electro-viscous effect is developed. This integration approach can be used on simple or complicated flow geometries. Resolution of the double layer is not needed in this approach, and the effects of the double layer can be accurately accounted for at the same time. With this approach, the numeric grid size can be much larger than the thickness of double layer. Presented in this paper are a description of the approach, model development, implementation, and several validation and demonstration simulations of pressure-driven Lab-on-Chip micro flows with electro-viscous effects.