Using in situ angle-resolved photoemission spectroscopy, we systematically studied molecular-beam-epitaxy-grown topological crystalline insulator SnTe(111) thin films with varied thicknesses and substrate conditions. An oscillation in the band gap size with an increase in thickness was observed to depend on the electric field perpendicular to the films. The observations are consistent with the theoretically predicted thickness- and electric-field-dependent topological phase transitions between the normal insulator and the quantum spin Hall insulator phases in SnTe(111) films and demonstrate them to be an excellent and electrically tunable quantum spin Hall system.