Field-effect transistors that employ an electrolyte in place of a gate dielectric layer can accumulate ultrahigh-density carriers not only on a well-defined channel (e.g., a two-dimensional surface) but also on any irregularly shaped channel material. Here, on thin films of 95% pure metallic and semiconducting single-walled carbon nanotubes (SWNTs), the Fermi level is continuously tuned over a very wide range, while their electronic transport and absorption spectra are simultaneously monitored. It is found that the conductivity of not only the semiconducting but also the metallic SWNT thin films steeply changes when the Fermi level reaches the edges of one-dimensional subbands and that the conductivity is almost proportional to the number of subbands crossing the Fermi level, thereby exhibiting a one-dimensional nature of transport even in a tangled network structure and at room temperature.