Defect-free, microporous Al2O3/SAPO-34 zeolite composite membranes were prepared by coating hydrothermally grown zeolite membranes with microporous alumina using molecular layer deposition. These inorganic composite membranes are highly efficient for H-2 separation: their highest H-2/N-2 mixture selectivity was 1040, in contrast with selectivities of 8 for SAPO-34 membranes. The composite membranes were selective for H-2 for temperatures up to at least 473 K and feed pressures up to at least 1.5 MPa; at 473 K and 1.5 MPa, the H-2/N-2 separation selectivity was 750. The H-2/CO2 separation selectivity was lower than the H-2/N-2 selectivity and decreased slightly with increasing pressure; the selectivity was 20 at 473 K and 1.5 MPa. The high H-2 selectivity resulted either because most of the pores in the Al2O3 layer were slightly smaller than 0.36 nm (the kinetic diameter of N-2) or because the Al2O3 layer slightly narrowed the SAPO-34 pore entrance. These composite membranes may represent a new class of inorganic membranes for gas separation.