We use classical molecular dynamics simulations to study the thermal boundary resistance (also known as Kapitza resistance) between graphene sheets (GS) either in octane or in vacuum. We found a higher value of Kapitza resistance for GS in vacuum compared to that in octane because the GS-GS interface has larger Kapitza resistance than the GS-octane interface, which is consistent with observations for carbon nanotube - carbon nanotube contacts. More importantly, the Kapitza resistance for the GS-GS contact can be 30% lower than values reported for the carbon nanotube - carbon nanotube contact. (C) 2012 Elsevier B.V. All rights reserved.