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We have fabricated sandwich type MgB2 Josephson junctions by using a Nb thin film as the counter electrode. The junction either contained a normal Au barrier layer or not. Superconducting MgB2 films were prepared on sapphire substrates by either in-situ annealing of cosputtered Mg and B mixture films or ex-situ diffusion annealing of B precursor films in Mg vapor. Surface of the MgB2 base film was mechanically dry-polished with 1/4 mum diamond powder to remove nonsuperconducting residues and subsequently cleaned by using argon ion beam. Junction was defined on an area of 4 mumtimes4 mum through a 150 nm thick SiOx insulating layer by lift-off and completed by depositing a normal thin Au layer (0~10 nm) and finally a 150 nm thick Nb counter electrode. Tc0 was at least 30 K for the MgB2 base electrode and 9 K for the Nb counter electrode. Current-voltage curves showed typical Josephson transition characteristics at critical currents. The junction critical current was modulated periodically in response to an applied magnetic field, in qualitative agreement with the theory of the Fraunhoffer diffraction.