Great attention is being shifted to Dye-sensitized solar cells because of their structural and electronic tunability, high performance, and low cost compared to conservative photovoltaic devices. In this work, the DFT/B3LYP/6-31G(d,p) and TD-DFT/mPW9PW91/6-31G(d,p) levels of theory are applied to the theoretical study of a new class of benzocarbazole-based D-A´-π-A dyes for their potential use in DSSCs. The influence of the internal acceptor on the optoelectronic properties is studied for the dyes. The optoelectronic and photovoltaic properties as HOMO, LUMO, E<sub>gap</sub> maximum absorption wavelength (λ<sub>max</sub>), vertical excitation energies (E<sub>ex</sub>), oscillator strength (<i>f</i>), light harvesting efficiency (LHE), open circuit voltage (V<sub>oc</sub>), injection force (ΔG<sub>inject)</sub>, were evaluated and discussed in order to compare their performance as DSSC sensitizers. The theoretical results show that all dyes exhibit excellent optoelectronic properties, such as a lower E<sub>gap</sub>(1.733 eV to 2.173 eV), a significant λ<sub>max</sub>(631.48 nm to 754.40 nm), a sufficient value of V<sub>oc</sub> (0.461 V to 0.880 V) and high LHE (0.853 eV to 0.968 eV). In particular M4 with 2,5-dihydropyrrolo [3,4-c]pyrrole-1,4-dithione as auxiliary acceptor has the potential to be used as a sensitizer for DSSCs, due to its red-shifted absorption spectrum (λ<sub>max</sub>= 754.40 nm), and small energy gap (E<sub>gap</sub>=1.733 eV). Indeed, this study may help chemists to synthesize efficient dyes for DSSC.