Abstract: An accelerated Landweber iterative thresholding algorithm in wavelet domain is proposed by using quadratic approximation of the fidelity term. In this algprithm, each iterate depends on a linear combination of the previous two iterates. Comparing with the standard iterative thresholding algorithm, the proposed algorithm is more effective and more flexible due to the alternatives of parameter. The numerical experiments show that the algorithm can improve the quality of the restored image effectively.