Double-sided superconducting MgB2 thin films are deposited onto c-Al2O3 substrates by the hybrid physical chemical vapour deposition method. The microwave response of MgBz/Al2O3 is investigated by microstrip resonator technique. A grain-size model is introduced to the theory of microstrip resonators to analyse microwave properties of the films. We obtain effective penetration depth of the films at 0K (λe0 = 463 nm) and surface resistance (R3 = 1.52mΩ at 11 K and 8.73 GHz) by analysing the resonant frequency and unload quality factor of the microstrip resonator, which suggests that the impurities and disorders of grain boundaries of MgB2/Al2O3 result in increasing penetration depth and surface resistance of the films.