This paper is concerned with the existence of the exact solution of the following nonlinear Volterra-Fredholm integral equation
is the unknown function, are the continuous nonlinear terms in a reproducing kernel space . Here is the space of absolutely continuous functions whose first derivative belongs of . The exact solution is given by the form of series. Its approximate solution is obtained by truncating the series and a new numerical approximate method is obtained. The error of the approximate solution is monotonously decreasing in the sense of . The intrinsic merit of the method given in this paper lies in its speedy convergence.