The ceramics of Sr3-xBaxSn2O7 (0 <= x <= 0.6) were synthesized by solid-state reaction method. The lattice constants of Sr3-xBaxSn2O7 increase with increasing of Ba doping. With increasing of the Ba2+ concentration from x = 0 to x = 0.2, the phase transition temperature reduces by 73 K. The vibration modes related to the phase transitions are strongly related to the tilting and rotation of SnO6 octahedra. The doping of Ba significantly aggravates the anharmonic effect and increases the Raman activity of the vibration mode A(2)((5)), and reduces the phonon lifetime and the Raman activity of the vibration mode A(1)((17)).