In this work the geometrical and electronic properties of (Carbazole-3.4-Ethylenedioxythiophene) (Cbz-Edot) based alternating donor-acceptor conjugated oligomers were studied by the density functional theory (DFT) at the B3LYP level with 6-31G(d) basis set. The acceptors investigated include thiazole (Z), thiadiazole (D), thienopyrazine (TP), thienothiadiazole (TD), benzothiadiazole (BT) and thiadiazolothienopyrazine (TPD). A low band gap will be expected in polymers containing donor-acceptor (D-A) repeating units. In order to predict the band gaps for guiding the synthesis of novel materials with low band gaps, we apply quantum-chemical techniques to calculate the band gaps in several oligomers. The results have been compared with those of thiophene and 3,4-ethylenedioxythiophene polymers with donor-acceptor fragment. The lowest excitation energies (Eex) and the maximal absorption wavelength (λabs) are studied using the time dependent density functional theory (TD-DFT), method. The electronic transitions of the absorption spectrum derived by TD-DFT method give useful structural and electronic information for designing novel conducting organic polymer materials. The theoretical results suggest that both the acceptor strength and the stable geometry contribute significantly to the electronic properties of alternating donor-acceptor conjugated copolymers.