A nanofluid is a fluid containing suspended solid particles, with sizes on the order of nanometers. Especially graphene nanoparticle that has the high thermal conductivity properties among the various nanoparticles added to the nanofluid is receiving attention. Graphene is a flat monolayer of $sp^2$-bonded carbon atoms tightly packed into a honeycomb lattice. And are known to have very high thermal conductivity. Therefore, we compared thermal conductivity with viscosity of graphene M-5 nanofluids and graphene M-15 nanofluids. Graphene M-5 and graphene M-15 have different average particle diameters and the other properties are the same. Two kinds of graphene nanofluids was examined by measuring thermal conductivity via transient hot-wire method. And the viscosity was measured by using a rotational digital viscometer. As a result, graphene M-5 nanofluids exhibited better thermal conductivity and viscosity than graphene M-15 nanofluids.