Polyimide-alumina composite membranes were fabricated by the nanotechnological copolymerization method of copolymer which has a constant repeating unit chemically bound by primer on the wall and/or surface of the porous ceramic support. By changing the number of repeating unit (n) in the polymer, the fabricated pyromellitic dianhydride (PMDA)-diaminodiphenylether (ODA) composite membranes have separation factor alpha(CO2/CH4) in the range 1.0-6.4 and molecular weight cut-off (MWCO) ranging 400-4000, As for the composite membranes of n = 20, the separation factor alpha(CO2/CH4) Of the 4,4＇-(hexafluoroisopropylidene)-diphathal anhydride (6FDA)-diaminodiphenylether (ODA) composite membrane was approximately 1.6 times larger than that of the PMDA-ODA composite membranes, and these values were 7.5 and 4.7 at 323 K, respectively. With the increase of temperature, the separation factor decreased, and the value obtained was 4.8 at 423 K. The pure gas permeances through the carbon membrane (PMDA-ODA : n = 20) was approximately 75-260 times larger than the values through the PMDA-ODA (n = 20) composite membranes. But this membrane did not show any gas separation ability.