Dye sensitizers can significantly affect power conversion efficiency of dye-sensitized solar cells (DSSCs). Porphyrin-based dyes are promising sensitizers due to their performances in DSSCs. Here, based upon a N-fused carbazole-zinc porphyrin-free-base porphyrin triad containing an ethynyl-linkage (coded as DTBC), the novel porphyrin dyes named DTBC-MP and DTBC-TP were designed by varying the porphyrin-free-base units in the conjugation of DTBC in order to study the effect of porphyrin-free-base in the modification of electronic structures and related properties. The calculated results indicate that, the extension of the conjugate bridge with the porphyrin-free-base unit results in elevation of the highest occupied molecular orbital (HOMO) energies, decrease of the lowest unoccupied molecular orbital (LUMO) energies, reduction of the HOMO-LUMO gap, red-shift of the absorption bands, and enhancement of the absorbance. The free energy changes demonstrate that introducing more porphyrin-free-base units in the conjugate bridge induces a faster rate of electron injection. The transition properties and molecular orbital characters suggest that the different transition properties might lead to a different electron injection mechanism. In terms of electronic structure, absorption spectra, light harvesting capability, and free energy changes, the designed DTBC-TP is a promising candidate dye sensitizer for DSSCs.