In present study, heat transfer and turbulent flow of water/alumina nanofluid in a counter flow double pipe heat exchanger have been investigated. The governing equations have been solved using CFD simulation, based on finite volume method. Single-phase and standard k-e models have been used for nanofluid and turbulent modeling, respectively. The internal fluid has been considered as hot fluid (nanofluid) and the external fluid, cold fluid (base fluid). The effects of flow direction and Reynolds number on base fluid, nanofluid and wall temperatures, and Nusselt number and convection heat transfer coefficient have been studied. The results indicated that increasing the Reynolds number causes enhancement of Nusselt number and convection heat transfer coefficient. In this study geometrical model is generated in the design modular in ANSYS 14.5 and the designed model is meshed in the ICEM CFD. Applying the desired boundary condition the meshed model has imported for CFD simulation and the results are analysed. Therefore, using of counter flow heat exchangers is recommended in higher Reynolds numbers.