In a dimerized Hubbard chain, we study the formation of the exciton band due to the Hubbard interaction by particle-hole scattering. The resonant level induced by Hubbard interaction is of the order of the interaction and exciton band appears. The band insulator - Mott insulator phase transition is discussed in the picture of the ground state, band gap, and exciton gap. With the same physics picture, we discuss the phase transition in a Hubbard chain with a staggered on site potential. The phase diagram was obtained in Phys. Rev. Lett. 83, 2014(1999) by M. Fabrizio, A.O. Gogolin, and A.A. Nersesyan. By density matrix renormalization group method, we obtained also numerical results that verified Fabrizio's phase diagram. At present, some details on the closing of band gap is still in scrutinizing.