We study the properties of exciton excitations in the Hubbard model with alteating potential and dimerized hopping terms at half filling. With increasing Coulomb repulsive, we find that a spin triplet exciton band develops below the band gap. At certain critical interaction, the excitation gap of this exciton band vanishes and a new phase with a dimerized ground state emerges. The value of this critical Coulomb interaction is determined perturbatively.