Superconducting MgB2 thin films were grown on single crystal Al2O3 (0001) by chemical vapour deposition using B2H6 as a boron source. MgB2 film was then accomplished by annealing the boron precursor films in the presence of high-purity magnesium bulk at 890℃ in vacuum. The as-grown MgB2 films are smooth and c-axis-oriented.The films exhibit a zero-resistance transition of about 38K with a narrow transition width of 0.2 K. Magnetic hysteresis measurements yield the critical current density of 1.9 × 107 A/cm2 at 10 K in zero field.