Electrical manipulation and detection of antiferromagnetic states have opened a new era in the field of spintronics. Here, we propose a noncollinear antiferromagnetic tunnel junction (AFMTJ) consisting of noncollinear antiferromagnetic Mn3Sn as electrodes and a bilayer boron nitride as the insulating layer. By employing the first-principles method and the nonequilibrium Green's function, we predict that the tunneling magnetoresistance (TMR) of the AFMTJ with AA- and AB-stacked boron nitride can achieve approximately 97% and 49%, respectively. Moreover, different orientations of the Néel vector in the electrodes lead to four distinct tunneling states in the Mn3Sn/bilayer BN/Mn3Sn AFMTJ. The TMR ratio could be notably improved by adjusting the chemical potentials, reaching up to approximately 135% at a chemical potential of 0.1 eV for the AFMTJ with AA-stacked boron nitride. This enhancement can be primarily attributed to the reduction in the transmission of antiparallel configurations around the K and K′ points in the two-dimensional Brillouin zone. Our findings could provide extensive opportunities for all-electrical reading and writing of the Néel vector of noncollinear antiferromagnets, paving the way for the development of antiferromagnetic tunnel junctions with two-dimensional tunnel barriers.