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This work is focused on the mass transport of methanol and the methanol-assisted crack healing in poly(methyl methacrylate) (PMMA)–graphene composites at different temperatures. The effect of the fraction of graphene on the mass transport of methanol and the methanol-assisted crack healing is also studied. The experimental results reveal that adding graphene to the PMMA matrix increases the resistance to the migration/diffusion of methanol and polymer chains in the PMMA matrix, and the absorption of methanol follows anomalous diffusion. The activation energies for the case I transport and case II transport in the PMMA–graphene composites are relatively independent of the fraction of graphene, and are larger than the corresponding ones in pure PMMA. Increasing the healing time and healing temperature allows for more polymer chains to migrate/diffuse across fractured surfaces, leading to the increase in the fracture strength of the crack-healed PMMA–graphene composites.