An algebraic method to construct the exact solutions of nonlinear differential-difference equations is presented by introducing the coupled Riccati equations. As an example, we apply this method to the general lattice equation, the relativistic Toda lattice equations and the (2+1) dimensional Toda lattice equation. Some kink solitary wave solutions and complexiton solutions are obtained with the help of symbolic system Mathematica. Our method can also be applied to other nonlinear differential-difference equations.