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.