Recent experimental investigation (Reitzenstein and Lambert,Macromolecules, 2009, 42, 773) indicated that the quite different optical properties of 2,7- and 3,6-linkage triarylboryl carbazole oligomers may arise from the different nature of their low-lying excited states: a low-lying delocalized within-backbone excitation in longer 2,7-linked oligomers vs a backbone-to-sidechain charge-transfer (CT) excitation independent of the polymerization length in 3,6-linked oligomers. Here in this paper, two long-range corrected functionals, CAM-B3LYP and ωB97X, are applied together with the traditional B3LYP functional in time-dependent density functional theory (TDDFT) calculations to systematically investigate the low-lying electronic excitations in both oligomers. Our calculations indicate that an extensive conjugation exists between monomer molecular orbitals in 2,7-linked oligomers, which is absent in those of 3,6-linked structures, resulting in a considerable narrowing of the HOMO-LUMO gap of their backbone moiety, while having little effect on the side-chains. CAM-B3LYP and ωB97x calculations confirm that the lowest-energy absorption is a within-backbone excitation in longer 2,7-linked oligomers as opposed to a backbone to side-chain charge transfer excitation in 2,7-linked oligmers of shorter length and 3,6-linked oligomers of any length. All these findings are consistent with the experimental findings and the qualitative energy diagram proposed by Reitzenstein and Lambert.