This work investigates the spectroscopic parameters, vibrational levels, and transition probabilities of 12 low-lying states, which are generated from the first dissociation limit, Br(P-2(u)) + O-(P-2(u)), of the BrO- anion. The 12 states are X-1 Sigma(+), 2(1)Sigma(+), 1(1)Sigma, 1(1)Pi, 2(1)Pi, 1(1)Delta, a(3)Pi, 1(3)Sigma(+), 2(3)Sigma(+), 1(3)Sigma(-), 2(3)Pi, and 1(3)Delta. The potential energy curves are calculated with the complete active-space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with Davidson modification. The dissociation energy D-0 of X-1 Sigma(+) state is determined to be approximately 26876.44 cm(-1), which agrees well with the experimental one of 26494.50 cm(-1). Of these 12 states, the 2(1)Sigma(+), 1(1)Sigma(-), 2(1)Pi, 1(1)Delta, 1(3)Sigma(+), 2(3)Sigma(+), 2(3)Pi, and 1(3)Delta states are very weakly bound states, whose well depths are only several-hundred cm(-1). The a(3)Pi, 2(3)Pi, and 1(3)Delta states are inverted and account for the spin-orbit coupling effect. No states are repulsive regardless of whether the spin-orbit coupling effect is included. The spectroscopic parameters and vibrational levels are determined. The transition dipole moments of 12-pair electronic states are calculated. Franck-Condon factors of a number of transitions of more than 20-pair electronic states are evaluated. The electronic transitions are discussed. The spin-orbit coupling effect on the spectroscopic parameters and vibrational properties is profound for all the states except for X-1 Sigma(+), a(3)Pi, and 1(1)Pi. The spectroscopic parameters and transition probabilities obtained in this paper can provide some powerful guidelines for observing these states in a proper spectroscopy experiment, in particular the states that have very shallow potential wells.