This study investigated the growth characteristics of carbon nanotubes (CNTs) by changing a period of annealing time and a $C_{2}H_{2}/H_2$ flow ratio at temperature as low as $450^{circ}C$ with inductively coupled plasma chemical vapor deposition. The 1-nm-thick Fe-Ni-Co alloy thin film served as a catalyst layer for the growth of CNTs, which was thermally evaporated on the 15-nm-thick Al underlayer deposited on the 50-nm-thick Ti diffusion barrier. The annealing at low temperature of $450^{circ}C$ brought about almost no granulation of the catalyst layer, and the CNT growth was not affected by a period of annealing time. A study of changing the flow rate of $C_{2}H_{2}$ and $H_2$ showed that as the ratio of the $C_{2}H_{2}$ flow rate to the $H_2$ flow rate was lowered, the CNTs were grown to be longer With further decreasing the flow ratio, the length of CNTs reached the maximum and then became shorter. Under the optimized gas flow rates, we successfully synthesized CNTs with a uniform length over a 4-inch Si wafer at $450^{circ}C$.