Continuous SSZ-13 zeolite membranes were reproducibly synthesized on the inner surface of 7-channel monolith supports for the first time. Packing density and mechanical strength were much greater than those using normal tubular and disc membranes. The membrane in the central channel of monolith was thinner than these of the side channels. The best monolith supported SSZ-13 membrane (with spacers) showed a CO2/CH4 selectivity of 72 and a CO2 permeance of 163 × 10-8 mol/(m2 s Pa) at pressure drop of 2.0 MPa and feed flow rate of 20 standard L/min for an equimolar CO2/CH4 mixture. Such separation performance was higher than most of zeolite membranes prepared on single-channel tubes or discs. The effects of temperature, pressure drop and fluid state on separation performance of the membranes were investigated. The extent of concentration polarization through monolith supported membrane was modelled by the concentration polarization index (CPI). Increasing feed flow rate and inserting spacers into the channels were effective ways to reduce the negative influence of concentration polarization. The latter way was more effective for our monolith supported membranes than the former because the dead volume was reduced greatly. Carbon dioxide permeance and CO2/CH4 selectivity increased by 24% and 85%, respectively, when the CPI increased from 0.79 (without spacer) to 0.89 (with spacer) at feed flow rate of 20 standard L/min.