We present here a lattice Boltzmann model with high Reynolds numbers in the presence of external force fields to describe electrokinetic phenomena in microfluidics, by considering pressure as the only external force for liquid flow. Our results from a 9-bit-square-lattice Boltzmann model are in excellent agreement with recent experimental data in pressure-driven microchannel flow that could not be fully described by electrokinetic theory. The difference between the predicted and experimental Reynolds numbers from pressure gradients are well within 5%. Our results suggest that the lattice Boltzmann model described here is an effective computational tool to predict the more complex microfluidic systems that might be problematic using conventional methods.