By virtue of the method of continuum limit,we obtained the solitons of the vibration of lattice in one-dimensional harmonic and anharmonic molecule chains，through which the equations of exciton and phonon are solved. On considering th e cubic anharmonic potential,the vibration of lattice in one\|dimensional mole cule chain has a solution of kink soliton and on considering the quartic anharm onic potential，the vibration of lattice in one-dimensional molecule chain has a so lution of breathers.