Deconvolution problem is a main topic in signal processing. Many practical applications are re-quired to solve deconvolution problems. An important example is image reconstruction. Usually, researcherslike to use regularization method to deal with this problem. But the cost of computation is high due to thefact that direct methods are used. This paper develops a trust region-cg method, a kind of iterative methodsto solve this kind of problem. The regularity of the method is proved. Based on the special structure of thediscrete matrix, FFT can be used for calculation. Hence combining trust region-cg method with FFT is suitablefor solving large scale problems in signal processing.