Cross-flow transport membrane condenser consisted of numerous ceramic membrane tubes is a novel device for heat and moisture recovery from flue gas. Fluid flow, heat and mass transfer in the membrane condenser are investigated by numerically solving the conservation equations for flue gas stream, membrane and water stream in a coupled way. Compared with the previous researches which neglected the variations of velocity, temperature and vapor fraction in the water flow direction, in this study the three-dimensional RNG k-ε turbulence model and laminar model are used in flue gas stream and water stream, respectively. The velocity, temperature and humidity contours of the membrane condenser, as well as the heat and water fluxes of the membrane surface are plotted. It is found that the variations of temperature, heat and mass fluxes on the membrane surface are significant. The latent heat flux accounts for more than 90% of the total heat flux. Besides, with the rise of flue gas velocity and packing fraction, the heat and water fluxes increase slightly, but the flow resistance of flue gas stream grows quickly. According to the analysis of thermal resistances, it is noticed that the thermal resistance at the water side is beyond 70% of the total resistance. The numerical results can provide the foundation for the engineering design and optimization of the transport membrane condenser.