We report on a new preparation method for magnesium diboride (MgB2) films by chemical vapour deposition(CVD) from diborane (B2H6). It is a two-step ex situ approach, with the precursor boron films grown by CVD from B2H6 at 460°C, followed by a post-annealing process in magnesium (Mg) vapour at 830°C. The prepared MgB2 thin films on Al2O3 polycrystalline substrates have an onset transition temperature of 35K and a zeroresistance temperature of about 24K. Well-crystallized MgB2 grains have clearly been observed in the SEM images and confirmed by x-ray diffraction analysis. The advantages of the proposed method are the feasibility to prepare large-area superconducting films and the compatibility with semiconductor technology.