Conjugate heat transfer of an automotive oil cooler with offset-strip fins was numerically investigated to predict the performance of the oil cooler for various flow-rates. The simulations were conducted by directly modeling offset-strip fins with unstructured meshes. The incompressible Navier-Stokes equations coupled with energy equation were used for the present simulations. Heat transfer characteristics of the oil cooler was compared well with experimental results and the errors were approximately within 5 percents. It was found that the performance of the oil cooler increased as the flow-rate increased up to the flow-rate of 12 L/min, but the performance seemed to be saturated beyond a critical flow-rate, which was estimated as 15 L/min. Furthermore, it was confirmed that compared to the performance without fins, that of the oil cooler with offset-strip fins was increased by about 75 percents.