Since single image restoration algorithms using lots of priori information lead to high complexity and low computational efficiency, a gradient cepstrum analysis method is proposed to estimate the point spread function PSF for a single blurred image. Firstly, we present the basic principle of estimating PSF from gradient cepstrum of a single blurred image and use the phase retrieval algorithm to recover phase information of the two-dimensional PSF, which can obtain the estimated PSF rapidly, Secondly, to evaluate the accuracy of the proposed PSF estimation method, the total variation regularized image restoration model coupling with an image gradient fidelity term is established and an alternating direction method with rapid and stable convergence is adopted to optimize the energy function. Both synthetic and real blurred images are tested to verify the performance of our scheme. Results show that our scheme not only can estimate the PSF rapidly and accurately so that it overcomes shortcomings of traditional algorithm with slow convergence, but also suppresses ringing effects to preserve information in edges. These advantages provide theoretical and technical foundation of the real engineering requirement in single image deblurring, especially for large scale images.