A new microscopic method based on the diabatic picture is proposed to describe the low-lying deformed excited 0^+ states in semi-magic nuclei. In this method, the couplings between anharmonic shape vibrations associated with different Hartree-Fock-Bogoliubov minima are diagonalized after constructing the diabatic basis. Basic ideas are illustrated for three kinds of exactly solvable models. Several examples are given which exhibit well localized deformed wave functions around the second minimum of the collective potential. It is possible that such deformed excited states well retain their identities against the mixing with the spherical configurations, even when their existence can hardly be expected from the properties of the adiabatic potential-energy functions.