We report the exotic photoluminescence (PL) behaviour of 3D topological insulator Bi2Te3 single crystals grown by customized self-flux method and mechanically exfoliated few layers (18 ± 2 nm)/thin flakes obtained by standard scotch tape method from as grown Bi2Te3 crystals. The experimental PL studies on bulk single crystal and mechanically exfoliated few layers of Bi2Te3 evidenced a broad red emission in the visible region from 600-690 nm upon 375 nm excitation wavelength corresponding to optical band gap of 2 eV. These findings are in good agreement with our theoretical results obtained using the ab initio density functional theory framework. Interestingly, the observed optical band gap is several times larger than the known electronic band gap of ~0.15 eV. The experimentally observed 2 eV optical band gap in the visible region for bulk as well as for mechanically exfoliated few layers Bi2Te3 single crystals clearly rules out the quantum confinement effects in the investigated samples which are well known in the 2D systems like MoS2,WS2, WSe2, and MoSe2 for 1-3 layers.