We propose an image reconstruction method for an X-ray telescope with an angular resolution booster proposed by Y. Maeda et al. at ISAS/JAXA. The booster consists of double coded masks in front of an X-ray mirror. In order to have a better sky image from an off-focus image, a proper image reconstruction process must be applied. The new image reconstruction method is based on the Bayesian statistics, where the traditional Richardson-Lucy algorithm is extended with a prior of sparseness and smoothness. Such a prior is desirable for astronomical imaging because astronomical objects have variety in shape from point sources, diffuse sources (supernova remnants, clusters of galaxies, and pulsar wind nebula) to mixtures of them (point sources in Galactic planes). As a result, the image resolution would be improved from a few arcmin to 10 arcsec. The performance of the X-ray telescope is demonstrated with simulated data: point sources and diffused X-ray sources such as Cas A and Crab Nebula. Through the demonstration, the angular resolution booster with the image reconstruction method is shown to be feasible.