MgB2 thin films were deposited on MgO (100) substrate and r-plane Al2O3 substrate by ex-situ annealing of boron film in magnesium vapor. The thickness of ex-situ annealed MgB2 films is approximately 600 nm according to data observation by ellipsometer. The magnetic properties of samples were determined using a vibrating sample magnetometer. The magnetic field dependence of the critical current density J (c) was calculated from M-H loops and also the magnetic field dependence of F (p) was compared for the different temperature ranges from 5 to 25 K. The critical current density J (c) was found to be around 1.0x10(6) A/cm(2) and 1.7x10(6) A/cm(2) in zero field at 5 K for MgB2 films deposited on MgO and r-plane Al2O3 substrates, respectively. It was found that the critical current density of the film deposited on MgO became stronger than that of r-plane Al2O3 in the magnetic field. The superconducting transition temperature was determined by ac susceptibility measurement using physical properties measurement system. ac susceptibility measurements for MgB2 films deposited on MgO and r-plane Al2O3 substrates were performed as a function of temperatures at constant frequency and ac field amplitude in the absence of dc bias field. The critical current densities as a function of temperature were estimated from the ac susceptibility data.