A high-performance and stable Co-based ZIF-67 membrane was successfully fabricated on a tubular substrate by ZnO-induced heteroepitaxial growth for the pervaporation separation of methanol (MeOH)/methyl tert-butyl ether (MTBE) mixture for the first time. Both the strong hydrophilicity and suitable pore size of the prepared ZIF-67 membrane allow methanol to be preferentially adsorbed and separated out from the MeOH/MTBE mixture. For the separation of 15 wt % MeOH/MTBE mixture, close to an azeotrope, the membrane exhibits a separation factor of as high as 3183 and high flux of 1.84 kg.m(-2).h(-1) at 40 degrees C, which is superior to almost all the reported membranes for the pervaporation separation of MeOH/MTBE mixture. More importantly, the ZIF-67 membrane with ZnO-linked special microstructure achieved by the heteroepitaxial growth could demonstrate excellent stability with the constant separation performance during the consecutive running over 70 h. Therefore, the high separation selectivity combined with its high stability makes the ZIF-67 membrane a promising candidate for the pervaporation separation of MeOH/MTBE mixture.