The interaction between a two-level atom trapped in symmetric double-well potential and a single mode cavity field is investigated. By solving Schrdinger equation, the analytical expressions of the total wave function and inversion of the atomic energy level for the whole system are given. Time evolution of the atomic population inversion is analyzed for different initial states of the cavity field, such as particle number, coherent and thermal states. Influence of atomic mass centre motion on population inversion is considered. Results show that by choosing appropriate cavity field initial state, potential well location and related factors, the spontaneous emission rate of an atom can be effectively controlled.