We investigated the effect of heteroleptic dual electron acceptor as a photosensitizer for the dye-sensitized solar cells (DSSCs). Novel tribranched organic dyes were designed with heteroleptic dual electron acceptors [cyanoacrylic acid (R-1), and indolinum carboxyl acid (R-2)] on each side of a triazine (TRZ) based organic dye and triphenylamine and the additional phenothiazine as an antenna group for DSSCs. The density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations were used to estimate the photovoltaic properties of the dyes. The absorption spectrum of the dyes showed different forms because of the different energy levels of molecular orbital (MO) of each dye and intramolecular energy transfer. Considering overall properties, the asymmetric tribranched organic dye exhibited a high conversion efficiency performance for DSSCs. The findings of this work suggest that optimizing the branch of electron donors and acceptors in dye sensitizers based on asymmetric tribranched organic dye produces good photovoltaic properties for DSSCs.