In this research convective heat transfer coefficient enhancement of nanofluids prepared from high surface area graphene has been investigated in laminar flow in the developing region. The nanofluid has been prepared from nanoporous graphene with high surface area and with concentration of 0.025 to 0.1wt.%. Deionized water has been used as the base fluid and a type of Ter-Polymer has been utilized as the surfactant. The results indicate that thermal conductivity of nanofluid with concentration of 0.1wt.% remains quite constant, with only 3.8% enhancement, while convective heat transfer coefficient improves significantly, with 34% enhancement. The behavior of this enhancement related to the concentration of graphene is linear. Also the results revealed that convective heat transfer coefficient of graphene nanofluids improves by temperature increase and the rate of improvement enhances by temperature increase. Increase in Reynolds number enhances the convective heat transfer.