We have studied the effects of the thickness of the graphene on the current-voltage characteristics of the carbon nanotube field effect transistors (CNT-FETs) with graphene contacts. It was shown that the CNT-FETs with thin graphene contacts showed larger drain ON current and transconductance than those of the devices with the thick graphene contacts. The result was explained by the inter-graphene resistance which dominates the contact resistance of the CNT-FETs with the graphene contacts. The inter-graphene resistance was estimated to be 2.2 Ω·cm2 from the extrinsic transconductance of the devices. © 2013 AIP Publishing LLC.