Surface roughness is present in most of the microfluidic devices due to the microfabrication techniques or particle adhesion. It is highly desirable to understand the roughness effect on microscale flow. In this study, we developed a three-dimensional finite-volume-based numerical model to simulate pressure-driven liquid flow in microchannels with rectangular prism rough elements on the surfaces. Both symmetrical and asymmetric roughness element arrangements were considered, and the influence of the roughness on pressure drop was examined. The three-dimensional numerical solution shows significant effects of surface roughness in terms of the rough elements' height, size, spacing, and the channel height on both the velocity distribution and the pressure drop. The compression-expansion flow around the three-dimensional roughness elements and the flow blockage caused by the roughness in the microchannel were discussed. An expression of the relative channel height reduction due to roughness effect was presented.