We propose an image reconstruction method for an X-ray telescope system with an angular resolution booster proposed by Maeda et al. (2018, PASJ, submitted). The system consists of double multi-grid masks in front of an X-ray mirror and an off-focused two-dimensional imager. Because the obtained image is off-focused, an additional image reconstruction process is assumed to be included. Our image reconstruction method is an extension of the traditional Richardson–Lucy algorithm with two regularization terms, one for sparseness and the other for smoothness. Such a combination is desirable for astronomical imaging because astronomical objects have a variety in shape, from point sources to diffuse sources to mixtures of both. The performance of the system is demonstrated with simulated data for point sources and diffuse X-ray sources such as Cas A and the Crab Nebula. The image resolution is improved from a few arcmin of focused image without the booster to a few arcsec with the booster. Through the demonstration, the angular resolution booster with the image reconstruction method is shown to be feasible.