<p>The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type. The method is based on the approximate solutions in terms of Chelyshkov polynomials with unknown coefficients. The Chelyshkov polynomials and their properties are employed to derive the operational matrices of integral and product. The application of these operational matrices for solving the mentioned problem is explained. The error analysis of the proposed method is investigated. Finally, some numerical examples are provided to demonstrate the efficiency of the method.</p>