We have fabricated high-quality c-axis-oriented $MgB_2$ thin films by using a pulsed laser deposition technique. The thin films grown on (1 1 0 2) $Al_2$$O_3$ substrates show an onset transition temperature of 39.2 K with a sharp transition width of ~0.15 K. X-ray diffraction patterns indicate a c-axis-oriented crystal structure perpendicular to the substrate surface. We observed high critical current densities ($J_{c}$) of ~ 16 $MA/ extrm{cm}^2$ at 15 K and under self-field, which is comparable to or exceeds those of cuprate high-temperature superconductors. The extrapolation $J_{c}$ at 5 K was estimated to be ~ 40 MA/$ extrm{cm}^2$, which is the highest record for $MgB_2$ compounds. At a magnetic field of 5 T, the $J_{c}$ of~ 0.1 $MA/ extrm{cm}^2$ was detected at 15 K, suggesting that this compound is very promising candidate for the practical applications at high temperature with lower power consumption. As a possible explanation for the high current-carving capability, the vortex-glass phase will be discussed.d.d.d.