Abstract: Firstly, based on Lax pairs of a class of differentialdifference equations, the N-fold Darboux transformation was constructed, and then we obtained the exact solutions of the equation by using  the  Darboux transformation.
 Through software drawing, we gave  the one, two, three and foursoliton solutions of the equation, and dicussed the 
elastic effect  among the three solitons and four solitons：  solitonic shapes and amplitudes do not change after  interaction.

Key words: differentialdifference equation, N-fold Darboux transformation, soliton solution