We present a simple, fast, and practical route to vertically align carbon nanotubes on a porous support using a combination of self-assembly and filtration methods. The advantage of this approach is that it can be easily scaled up to large surface areas, allowing the fabrication of membranes for practical gas separation applications. The gas transport properties of thus constructed nanotube/polymer nanocomposite membranes are analogous to those of carbon nanotube membranes grown by chemical vapor deposition. This paper shows the first data for transport of gas mixtures through carbon nanotube membranes. The permeation of gas mixtures through the membranes exhibits different properties than those observed using single-gas experiments, confirming that non-Knudsen transport occurs.