In this paper, we consider a linear operator equation with noisy data and use a modified iterative Landweber method as an iterative solver. We used polar decomposition to get a symmetric positive definite operator and used instead of identity operator in classical Landweber method. The necessary analysis of the convergence of the iteration method was carried out. The residual method used as a stopping rule for the iterations. The modified iterative method compared to the classical Landweber. A numerical experiment illustrates the effectiveness of this method by applying it for solving the inverse boundary value problem of heat equation.