Abstract: In this research we use the numerical solution method that is based on Chebyshev polynomials and Legendre polynomials, to solve non-singular integral equation, it is known as Fredholm integral equation of the second kind. We use these expansions because of their convergence and recurrence properties. Also both of them can be represented as trigonometric function on [1, -1]. First, we expand the unknown function in the integral equation based on the related formulas, then develop kernel of integral equation. To find these, we should try to find a function which can be represented as the solution of linear differential equations. Then substitution into the integral equation, we find the coefficients of the function. At the end of research the method will be illustrated by the mean of an example.