In the present paper we study the approximate solution for Fredholm integral equation of the second kind in the space L2p(x)[0,2π] with weight function p (x) ≥ 1 and bounded almost every where on [0,2π]. The technique of this study is based on linear polynomial operators Un (φ; x) which generate good approximation to the function φ (x) in the space L2p(x)[0,2π], where the given equation is replaced by Fredholm integral equation with degenerate kernel. The solution of the new equation is taken as an approximate solution to the original equation, and also we give estimates of the errors which arise in this connection. This approximation is discussed in details for Dirichlet, Vallee-Poussin, Féjer, Rogozinski and Jackson operators.