Bi2Se3 with highly thermoelectric power is, recently, known for its properties of three-dimensional topological insulator. In this thesis, we report that the terahertz wave can be generated from the surface of Bi2Se3 and Cu-doped Bi2Se3 single crystals by the femtosecond optical pumping pulses at 800 nm. Furthermore, the terahertz output power is strongly dependent on the carrier concentrations. The THz wave generated from the Cu-doped Bi2Se3 with carrier concentration ~1018 cm-3 is nearly ten times higher than that from the pure Bi2Se3 with carrier concentration ~1019 cm-3. The THz generation mechanism on the pure, Cu-doped Bi2Se3 and even the correlation between THz wave generation and the surface state of topological insulator will be discussed in this thesis.