n this study a numerical method is developed to solve the Hammerstein integral equations. To this end, the kernel has been approximated using the least-squares approximation schemes based on Legendre-Bernstein basis. The Legendre polynomials are orthogonal and this property improves the accuracy of the approximations. Also the nonlinear unknown function has been approximated by using the Bernstein basis. The useful properties of Bernstein polynomials help us to transform Hammerstein integral equation to solve a system of nonlinear algebraic equations.
