In non-adiabatic cases the topological action associated with Berry's phase and the corresponding effective Hamiltonian are obtained by path-integral method. We also give the non-adiabatic transition probability amplitude in the first-order approximation. It is thereby shown that the Berry's phase and the induced gauge structure have universality of existence. As an example, dynamics of induced monople relating to the Bitter-Dubber's experiment is analysed in terms of induced gauge field.