Bi2Se3 as a well-known topological insulator has become the focus of research especially on its transport properties. It is a narrow band gap semiconductor with conducting states on its surface. However, studies on its optical spectra, including excitonic effects, are very limited for this material. One of the reasons may be that such calculations are rather computationally demanding. In this work, we use density functional theory (DFT) as implemented in Quantum Espresso package to calculate the ground state properties of this material. We also calculate its optical spectra using Yambo code. As we are interested in exploring the excitonic effects, we incorporate electron-hole interactions by solving the Bethe-Salpeter equation. To obtain accurate results with inexpensive calculations we implement a double-grid method in dealing with k-point integration. Assuming that electron-electron interaction is effectively screened in this system, we do not treat the electron-electron interaction beyond the exchange-correlation functional within the DFT.