This paper is develops an effective method based on two-dimensional Chelyshkov polynomials (2DCPs) to provied an approximate solution of a class of nonlinear two-dimensional Volterra Integral equations of the first kind. This problem is transformed to a nonlinear two-dimensional Volterra Integral equations of the second kind. The method transforms the integral equation to a system of nonlinear algebraic equations by means of collocation points. Finally, some numerical examples are given to clarify the efficiencey of the presented method.