To ascertain membrane distillation (MD) as an emerging desalination technology to meet the global water challenge, development of membranes with ideal material properties is crucial. Functionalized carbon nanotubes (CNTs) were anchored to nanofibres of electrospun membranes. Covalent modification and fluorination of CNTs improved their dispersibility and interfacial interaction with the polymer membrane, resulting in well-aligned CNTs inside crystalline fibres with superhydrophobicity. Consideration for the chemical/physical properties of the CNT composite membranes and calculation of their theoretical fluxes revealed the mechanism of MD: CNTs facilitated the repulsive force for Knudsen and molecular diffusions, reduced the boundary-layer effect in viscous flow, and assisted surface diffusion, allowing for fast vapor transport with anti-wetting. This study shows that the role of CNTs and an optimal composite ratio can be used to reduce the gap between theoretical and experimental approaches to desalination.