We introduce the variational iteration method for solving the generalized Degasperis-Procesi equation. Firstly, according to the variational iteration, the Lagrange multiplier is found after making the correction functional. Furthermore, several approximations of $u_{n+1}(x,t)$ which is converged to $u(x,t)$ are obtained, and the exact solutions of Degasperis-Procesi equation will be obtained by using the traditional variational iteration method with a suitable initial approximation $u_0(x,t)$. Finally, after giving the perturbation item, the approximate solution for original equation will be expressed specifically.