The two-dimensional integro-differential partial equations is one of the so difficult problems to be solved analytically and/or approximately, and therefore, a method that is efficient for solving such type of problems seems to be necessary. Therefore, in this paper, the iteration methods, which is so called the variational iteration method have been used to provide a solution to such type of problems approximately, in which the obtained results are very accurate in comparison with the exact solution for certain well selected examples which are constructed so that the exact solution exist. Main results of this work is to derive first the variational iteration formula and then analyzing analytically the error term and prove its convergence to zero as the number of iteration increases.
