In this paper, we present a new analytical technique to obtaining the analytical approximate solutions for system of Fredholm integral equations based on the use of the Gauss Lobatto Method for approximating. We used a compute of approximate roots of Legendre polynomial by recursive relation. In the iterative method, we chose a good initial guess and initial approximation. We create the new efficient method for solving Fredholm integral and integrodifferential equations of the second kind and the systems which consist such equations.