The pressure-induced superconductivity and structural evolution of Bi2Se3 single crystals are studied. The emergence of superconductivity at an onset transition temperature (Tc) of about 4.4 K is observed at around 12 GPa. Tc increases rapidly to a maximum of 8.2 K at 17.2 GPa, decreases to around 6.5 K at 23 GPa, and then remains almost constant with further increases in pressure. Variations in Tc with respect to pressure are closely related to the carrier density, which increases by over two orders of magnitude from 2 to 23 GPa. High-pressure synchrotron radiation measurements reveal structural transitions at around 12, 20, and above 29 GPa. A phase diagram of superconductivity versus pressure is also constructed.