Seismic image, especially for the prestack image, performs a blurred version of the reflectivity image due to spatial aliasing, poor acquisition aperture, and nonuniform illumination. The blurring effects can be quantified by the point spread function (PSF). We herein adopt an explicit space-variant PSF formula, which can be defined as a sequential application of the modeling and migration operators with the asymptotic Green's function. The deblurred images are restored using the nonstationary deconvolution with total variation regularization in which the blurred images are described by the convolution between the space-variant PSF and the reflectivity image. However, nonstationary deconvolution is computationally challenging. We introduce an extending primal-dual hybrid gradient (E-PDHG) method to decompose the complex problem into a sequence of simple subproblems that have closed-form solutions. Numerical results on synthetic data and field data demonstrate that the proposed E-PDHG method outperforms the basic PDHG method in the prestack seismic image deblurring.