The membrane-based total heat exchanger is a device to recover both sensible heat and moisture from the exhaust air stream from a building. Heat and mass transfer intensification has been undertaken simultaneously in two directions: air-side augmentation with cross-corrugated triangular ducts and material-side augmentation with a novel composite-supported liquid membrane (CSLM). Performance of heat and mass transfer intensification has been investigated numerically. As a first step, the convective heat and mass transfer coefficients in the flow passages are calculated. Then, the heat and moisture diffusion resistance through the CSLM itself is estimated. Finally, the sensible and moisture-recovery effectiveness are obtained with effectiveness-NTU (number of transfer units) methodology. It is found that the new concept of cross-corrugated triangular ducts with CSLM has a 14% higher sensible effectiveness and a 46% higher latent effectiveness in comparison with a traditional total heat exchanger of parallel plates with a common solid membrane.