In this paper, we study the numerical approximation of a class of nonlinear integral equations of Volterra type called nonlinear functional Volterra Urysohn integral equations. Using a technique based on the Picard iterative method, the existence and uniqueness of the solution to the equation was proved. For the numerical approximation of the solution, we used the collocation method with sigmoidal functions. By using a Gronwall inequality, the convergence of the method is proved. At the end, some numerical examples are presented to show the effectiveness of the method.
