We have fabricated the superconducting $MgB_2$/carbon fiber by physical vapor deposition method. Mg (Magnesium) and B (Boron) were simultaneously deposited on the carbon fiber using the RF-sputtering and thermal evaporation, respectively. To ensure the relatively high vapor pressure of Mg at the growth region and the subsequent phase stability of $MgB_2$ at the deposition temperature, inverted funnel-like guide made of Mg-foil was employed while one side of the guide were open for the sputtered B flux. Mg vapor pressure should be controlled precisely to secure the complete reaction. The $MgB_2$/carbon fiber showed a uniformly deposited thin layer with dense and well-formed grains. The $MgB_2$/carbon fibers in this study showed $T_c$~37.5K, $J_c$ ~ $2{ imes}10^4;A/cm^2$ in the 20K, 0T.