A porous $alpha$-alumina tube of 2.5 mm O.D. and 1.9 mm I.D. was used as the support of an inorganic membrane. Macropores of the tube, about 150 nm in size, were plugged with silica formed by thermal decomposition of tetraethylorthosilicate at $600^{circ}C$. The forced cross-flow CVD method that reactant was evacuated through the porous wall of the support was very effective in plugging macropores. The H$_2$ permeance of the prepared membrane was of the order of $10^{-8}/ molㆍs^{-1}/ㆍm^{-2}/. Pa{-1}$/, while the $N_2$ permeance was below $10^{-11}/ molㆍs^{-1}/ㆍm^{-2}/ㆍPa^{-1}$/ at $600^{circ}C$. This was comparable to that of silica-modified Vycor glass whose size was 4 nm.