Since the discovery of its superconductivity, magnesium diboride (MgB2) has been identified as a promising superconductor to be used in Josephson junction devices due to its high transition temperature, large energy gap, long coherence length, and expected easier fabrication of Josephson junctions as compared with high temperature superconductors. The high-quality MgB2 films and excellent tunnel barrier materials are the core elements for a Josephson junction. Here in this paper, all MgB2 thin film tunnel junctions with B tunnel barriers are fabricated in situ on sapphire substrates and their tunneling characteristics re investigated. The experimental results indicate that the MgB2/B/MgB2 junctions exhibit good tunneling characteristics. The deposition of the MgB2/B/MgB2 trilayer is carried out in a completely in situ process. The bottom and top MgB2 layers are grown to a thickness of 100 nm by hybrid physical-chemical vapor deposition (HPCVD) technique at about 973 K and in 102 Pa Ar atmosphere on a single crystal Al2O3 (0001) substrate. The 35-nm-thick amorphous B insulator layer is deposited using chemical vapor deposition method at 723 K and in 103 Pa pure Ar. In the process of the top MgB2 layer deposition, the amorphous B reacts with Mg in Mg vapor, leading to its thickness decreasing to 10 nm. Square-shaped junctions each with a size of 4 mm5 mm are determined by the metallic mask method. The resistivity temperature (R-T) curves and the DC current-voltage (I-V) curves of the MgB2/B/MgB2 junctions at different temperatures are measured by the four-point probe method in the physical property measurement system (PPMS). The experimental results show excellent superconducting properties of the top and bottom superconductor with high Tc (above 39.5 K), appreciable Jc values (107-108 A/cm2). In the I-V characteristics of junction at temperatures ranging from 4.2 K to 39.2 K, the junctions exhibit clear Josephson tunneling characteristics with jc～0.52 A/cm2 at 4.2 K, which remains nonzero up to 31.3 K. The hysteresis is pronounced at 4.2 K, becoming smaller as temperature increases, and eventually disappearing at around 19.2 K. By using the differential I-V curves, only gap is observed in differential conductance vs. voltage characteristics (dI/dV-V) curves, because MgB2 layer grown using HPCVD technique is always c-axis oriented and more than 99% contribution to the conduction is from band charge carriers.