Forest of single-walled carbon nanotubes (SWNTs) was grown at $450^{circ}C$ by water-plasma chemical vapor deposition using ultrathin iron on alumina supporting film. The growth rate of the SWNT forest is ${sim}0.9;{mu}m/min$, and the diameters of nanotubes are mainly in a range of 3.0 ~ 3.5 nm. The low intensity ratio of D- to G-band ($I_D/I_G$ ~ 0.098) in Raman spectra indicates that our SWNT forest grown at $450^{circ}C$ is fairly pure and crystalline. This low temperature growth of SWNT forest may enable variable applications requiring the vertically-aligned nanotubes to obtain large surface area.