Films composed of super-aligned single-walled carbon nanotubes (SWCNTs) have been widely used in electronic devices. Using first-principles calculations, we investigate the energetically most favorable stacking patterns and the electronic structures of SWCNT monolayers and bilayers formed by super-aligned (5, 5) and (7, 0) SWCNTs. It is found that the (5, 5) SWCNT monolayer prefers a ‘face-by-face’ stacking pattern with the binding energy of 13.90 meV/atom, whereas the (7, 0) SWCNT monolayer favors an ‘edge-by-edge’ pattern with the binding energy of 10.82 meV/atom. The (5, 5) SWCNT arrays are semiconducting with a band gap up to 114 meV for the bilayer, while the (7, 0) SWCNT arrays are metallic with a tiny overlap between valence and conduction bands, in sharp contrast to the cases of isolated (5, 5) and (7, 0) SWCNTs. This implies that weak van der Waals interactions between SWCNTs play an important role in applications of SWCNT films in electronic devices.