The nanocomposites with reversible cross-linking covalent bonds were prepared by reacting furfurylamine (FA)-modified diglycidyl ether of bisphenol A (DGEBA) and furfuryl-functionalized aniline trimer-modified graphene (TFAT-G) with bismaleimide (BMI) via Diels-Alder (DA) reaction. The successful synthesis of the TFAT modifier is confirmed by NMR hydrogen spectroscopy and IR spectroscopy tests. The structure and properties of TFAT-G epoxy nanocomposites are characterized by SEM, DSC, tensile and resistivity CES. The results show that TFAT-G was uniformly dispersed in the resin, and 1wt% TFAT-G composites increase to 233% for tensile strength, 63% for elongation at break, 66.1% for modulus and 7.8℃ for Tg. Overall, the graphene/self-healing resin nanocomposites have both good self-healing function and electrical conductivity by adding 1% modified graphene and still maintain the original 83% strength and 89% electrical conductivity after one cycle of heating repair.