Free-standing graphene carbon membrane with conch nacre structure was prepared via carbonizing composite membrane of graphene oxide (GO) and polyamide acid (PAA) obtained by solvent evaporation method at 600℃. The morphology and structure were characterized by XRD and SEM. The permeation performance of CO2 and CH4 of free-standing graphene carbon membrane with different PAA solid content was investigated. The results indicated that GO was thermally reduced to graphene in graphene carbon membrane after carbonization, in which graphene layers were lamellar stacked and gaps between layers were filled with holes and carbon residue. Both CO2 permeability and ideal selectivity for the CO2/CH4 of graphene carbon membranes were enhanced with increasing PAA solid content. The CO2 flux of graphene carbon membrane was up to 824 barrer and the CO2/CH4 ideal selectivity reached 38.9 simultaneously. The gas permeation channels of graphene carbon membrane were attributed to the lamellar stacked of graphene and carbon molecule sieve in graphene carbon membrane. This study opened up new opportunities to prepare the flexible free-standing graphene carbon membrane for gas separation.