A numerical method for solving nonlinear system of Fredholm-Volterra Hammerstein integral equations of second kind is presented. This method is based on replacement of the unknown functions by truncated series of well known Chebyshev expansion of functions. The quadrature formula which we use to calculate integral terms can be estimated by Fast Fourier Transform (FFT). Also, convergence and rate of convergence are given. The numerical examples and the number of operations show the advantages of this method to all other recent works which use operational matrices (with huge number of operations) or solving special case of nonlinear system of integral equations.

nonlinear system of Fredholm-Volterra integral equations, Chebyshev polynomials, error analysis.