The combination and balance of acceptor (A)-bridge- donor (D) structure of molecule confer suitable attributes and properties to act as efficient light-harvesting and sensitizers in dye sensitized solar cells (DSSCs). An important performance is the electron photo injection (PI) mechanism which can take place either via type I (indirect), that contains in injecting from the excited state of the dye to the semiconductor upon photo excitation. Here, we present a computational study to find the molecular optimization, electronic structures, optical properties of metal free organic dye sensitizer (2E)-3-(4-(4-methoxystyryl) phenyl)-2- cyanoacrylic acid was studied based on Hartree-Fock (HF) and DFT calculation using the hybrid functional B3LYP. UV-Vis spectrum was investigated by time dependent-density functional theory (TD-DFT). The theoretical results has shown that TD-DFT calculations using the polarizable continuum model (PCM) were reasonably capable of predicting the excitation energies, the absorption and the emission spectra of the molecules. Features of the absorption spectrum in the visible and near-infrared regions were assigned based on TD-DFT calculations. The absorption bands absorption bands are mainly derived due to the assigned transition between to n →π*.