Heat transfer performances of viscoelastic fluid, water-based Cu nanofluid, and viscoelastic-fluid-based Cu nanofluid flows in a circular pipe at a Peclet number of 40,000 were experimentally studied. It indicates that the viscoelastic fluid turbulent flow gives great heat transfer reduction, while the water-based Cu nanofluid flow shows significant heat transfer enhancement. The viscoelastic-fluid-based Cu nanofluid also exhibits heat transfer enhancement as compared with viscoelastic base fluid flow. The effects of nanoparticle volume fraction, mass concentration of viscoelastic base fluid, and temperature on local convective heat transfer coefficient and possible heat transfer enhancement mechanisms of nanofluid flows were discussed.