The X3g- and A3u states of B2 molecule are studied using highly accurate valence internally contracted multireference configuration interaction approach including the Davidson modification. The Dunning's correlation-consistent basis sets, aug-cc-pV6Z and aug-cc-pV5Z, are used in the study. To obtain more reliable results, the potential energy curves (PECs) of two electronic states are extrapolated to the complete basis set limit by the two-point total-energy extrapolation scheme. The effects of the core-valence correlation and relativistic correction on PEC are taken into account. Employing these PECs, the spectroscopic parameters (Te, Re, e, exe, eye, Be, e, e and e) of the X3g- and A3u states of two main isotopes (11B2, 10B11B) are determined and compared with those reported in the literature. Comparison with the experimental data demonstrates that the present results are accurate. With the PECs determined here, the whole vibrational states for 11B2 (X3g-, A3u) and 10B11B (X3g-, A3u) are determined when the rotational quantum number J equals zero (J=0) by numerically solving the radical Schrdinger equation of nuclear motion. For each vibrational state of every isotope species, the vibrational level and inertial rotation constants are obtained, which are in excellent accordance with the experimental findings.