A general nonlinear functional integral equation has been studied. The considered equation is of Fredholm type and includes some well-known integral or functional equations, as special cases. By assuming some smoothness conditions on the functions in the equation, we prove the existence and uniqueness of the solution by means of a fixed point method. Then, we apply the so-called Nyström method in order to approximate the solution, which leads to a system of nonlinear algebraic equations. In the next step, the Picard iteration method is utilized for approximating the solution of the resulting system of nonlinear algebraic equations. The convergence of the numerical scheme is proved, its computational complexity is computed and finally some illustrative examples are included to demonstrate the efficiency and applicability of the technique
