A comprehensive theoretical treatment is presented of the low-lying electronic states of the molecular ion BBr+correlating with the two lowest dissociation asymptotes B+(1S) Br(2P) and B(2P)+Br+(3P). All-electron CASSCF+CI calculations have been made with averaged atomic natural orbital basis sets. Spectroscopic constants are calculated for the bound states but are in disagreement with an experimental analysis in the literature of a2Πr→ X2Σ+system. It is suggested that a re-examination of the spectroscopy of this species would be worthwhile.