By using the Fermi-Bose transformation, the antiferromagnetic chain is mapped into the bosonic field, and the energy density of the ground state and the excite states of the model are given. The relationship between the energy density of the ground state and the strength of distortion of the model is obtained. The results show that there exists a spin-Peierls transition in the model. Finally, the numerical simulation is performed to verify the above theoretical prediction.