Superconducting $MgB_2$ fibers are in-situ grown by a diffusion method. The fibers are prepared by exposing B filaments to Mg vapor inside a folded Ta foil over a wide range of temperature and growth time. The materials are sealed inside a quartz tube by gas welding. The as - grown fibers are characterized by scanning electron microscopy and energy dispersive x - ray analysis. The fibers have a diameter of about $110{mu}m$. Surface morphology of the fibers looks dependent on growth temperature and mixing ratio of Mg and B. Radial distribution of Mg ions into B is observed and analyzed over the cross - sectional area. Transport properties of the $MgB_2$ fibers are examined by a physical property measurement system. The $MgB_2$ fibers grown at $900^{circ}C$ for 2 hours show a superconducting transition at 39.8K with ${Delta}T_c<$ 2.0 K. Resistance at room temperature $MgB_2$ is 3.745 $Omega$ and residual resistivity ratio (RRR) is estimated as 4.723.