Ab initio calculations on the ground and valence excited states of the GaBr molecule have been performed by using the entirely uncontracted all-electronic aug-cc-pVQZ basis sets and the internally contracted multireference singles and doubles configuration interaction method with Davidson size-extensivity correction and Douglas-Kroll scalar relativistic correction. The potential energy curves of all valence states and the spectroscopic constants of bound states are fitted. It is the first time that the entire 23 Omega states generated from the 12 Lambda-S states of the GaBr molecule are studied in a theoretical way. Calculation results well reproduce most of the experimental data. The effects of the spin-orbit coupling and the avoided crossing rule between Omega states of the same symmetry are analyzed. The observed diffuse absorption bands near 36000 cm(-1) can be contributed to the transitions from the C1(II) and other higher shallow potential well excited states, lying at the region of about 34000-38000 cm(-1), to the ground state. The transition properties of the A(3)Pi(0+) and B(3)Pi(1) states to the ground-state transitions are predicted for the first time, including the transition dipole moments, the Franck-Condon factors and the radiative lifetimes. The lifetime of the A(3)Pi(0+) state of the GaBr molecule is of the order of milliseconds, while that of the B(3)Pi(1) state is of the order of microseconds.