In order to investigate the catalytic mechanism for the growth of carbon nanotubes (CNTs), a comprehensive study was conducted using carbon materials synthesized at 680 ${^{circ}C}$ with a gas mixture of CO-H$_2$ after reduction at 800 ${^{circ}C}$ by H$_2$ gas from iron oxide, and metal Pt. The resulting material was observed by scanning electron microscopy (SEM) and X-ray diffraction patterns (XRD) after a variety of reaction times. The carbon materials synthesized by metal Pt were little affected by reaction time and the sintered particles did not form CNTs. Xray analysis revealed that metal Fe was completely converted to iron carbide (Fe$_3$C) without Fe peaks in the early stage. After 5 min, iron carbide (Fe$_3$C) and carbon (C) phases were observed at the beginning of CNTs growth. It was found that the intensity of the carbon(C) peak gradually increased with the continuous growth of CNTs as reaction time increases. It was also found that the catalyst of growth of CNTs was metal carbide.