Introduction: The theory and application of nonlinear integral equations is an important subject within physics and applied mathematics. There are several numerical approaches for solving nonlinear integral equations. Aim: In this paper, a new set oforthogonal functions of hybrid functions of block-pulse functions and Legendre polynomials (HBL), is applied to numerical solution of nonlinear integral equations. Materials and Methods: The properties of HBL are first presented. These properties together with operational matrix for integration and product operation matrix utilized to reduce the solution of nonlinear integral equations to the solution of algebraic equations system. Results: Its accuracy and applicability were checked on some examples. The numerical results show that the accuracy of the solutions obtained is good. Conclusion:Finally, the method can be easily extended and applied to systems of nonlinear integral equations, linear and nonlinear integro-differential equations and systems of linear and nonlinear integro-differential equations with suitable initial conditions. Keywords
