The AFI membrane with one-dimensional straight channels is an ideal platform for various applications. In this work, we report the fabrication of a highly c-oriented, compact and stable AFI membrane by epitaxial growth from an almost close-packed and c-oriented monolayer of plate-like seeds that is manually assembled on a porous alumina support. The straight channels in the membrane are not only aligned vertically along the membrane depth, but are also continuous without disruption. The transport resistance is thus minimized and as a result, the membrane shows almost two orders of magnitude greater permeance in pervaporation of hydrocarbons compared to reported values in the literature. The selectivity of p-xylene to 1,3,5-triisopropylbenzene (TIPB) is approximately 850. In addition, through gas permeation studies on a number of gas and liquid molecules, different transport mechanisms including activated Knudsen diffusion, surface diffusion and molecular sieving were discovered for different diffusion species. The ratio of kinetic diameter to channel diameter, dm/dc, and the ratio of the Lennard-Jones length constant to channel diameter, σm/dc, are found very useful in explaining the different transport behaviors. These results should be useful not only for potential industrial applications of the AFI membranes but also for the fundamental understanding of transport in nanoporous structures.