The critical Josephson currents in a S 1 /N/S 2 double interfaces tunnel junction are calculated by using the linearized Usadel equation to derive the anomalous Green‘s function in the normal-metal layer (N). Both of the S 1 and S 2 layers are formed by MgB 2 but due to the proximity effect have different characteristics. Two orientations of the MgB 2 superconductors are considered. In one junction, the c-axis of MgB 2 in the S-layer is perpendicular to the interface, while in the other, the ab-plane is perpendicular to the interface. The different transparencies of the two MgB 2 /normal-metal interfaces, the normal state resistances of the currents flow from S 1 to S 2 in each band and the N-layer thickness are taken into account. The critical Josephson currents in both the c-axis and ab-plane oriented junctions are studied near the critical temperature. The predicted currents are compared with the experimental currents and are seen to fit the data above 0.4T C .