All MgB2 Josephson junctions with amorphous boron barriers have been fabricated on C-plane sapphire substrates by using a co-evaporation method. The junctions showed Josephson currents and the nonlinear current-voltage characteristics which seem to reflect the superconducting energy gap. The critical current was observed when the thickness of the amorphous boron was in the range of 5 nm to 20 nm. The critical current density was estimated to be 0.4 A/cm2 to 450 A/cm2. By observing he temperature dependence of the critical current we found that the junction had a critical temperature of 10 K and a normal layer in its barrier structure.