The shrinking physical scale of microfluidic chips brings significant benefits like less expense of chemicals, shorter diagnosing time and highly parallel testing, but at the same time presents big challenges in drag reduction and thermal management. The ridge/groove structure on the superhydrophobic surface inside microchannels, which entraps air so as to reduce the skin friction, is believed to affect the internal heat transfer. In the current study, the flow and heat transfer between two walls with eccentric transverse microgrooves was studied based on numerical simulations, to investigate its effect on overall drag reduction, heat transfer enhancement and possible mechanisms. The changes in drag reduction capability and convective heat transfer were respectively evaluated in terms of the effective slip length and Nusselt number. The overall thermal performance and efficiency were evaluated using the goodness factor. It was found that the eccentricity of transverse microgooves inside superhydrophobic channel increases the effective slip length but reduces heat transfer slightly, which is especially obvious at low Reynolds number, large pattern length and moderate shear free fraction. Besides drag reduction and heat transfer, the flow fields for different cases were investigated in details, which show that the increase in the effective slip length of superhydrophobic microchannel with offset can be attributed to the increase of average velocity on air-water interface.