In this paper, we study the numerical solution of Fredholm integral equations of the first kind with convolution kernel by using preconditioned conjugate gradient (PCG) method. Then by using quadrature method the integral equations reduce to a Toeplitz system. In the case that the coefficient matrix of above system is symmetric positive definite (SPD), we can use CG method for solving the system. At normal state, the system contains in appropriate eigenvalues not clustering around 1. The using of CG method with suitable preconditioners causes clustering eigenvalues of the new system around 1. As a result, the stability and convergence rate are guaranteed.
