Many exoplanets have been found in orbits close to their host stars and thus they are subject to the effects of photo-evaporation. Previous studies have shown that a large portion of exoplanets detected by the Kepler mission have been significantly eroded by photo-evaporation. In this paper, we numerically study the effects of photo-evaporation on the orbital evolution of a hypothesized moon system around a planet. We find that photo-evaporation is crucial to the stability of the moon system. Photo-evaporation can erode the atmosphere of the planet thus leading to significant mass loss. As the planet loses mass, its Hill radius shrinks and its moons increase their orbital semi-major axes and eccentricities. When some moons approach their critical semi-major axes, global instability of the moon system would be triggered, which usually ends up with two, one or even zero surviving moons. Some lost moons could escape from the moon system to become a new planet orbiting the star or run away further to become a free-floating object in the Galaxy. Given the destructive role of photo-evaporation, we speculate that exo-moons are less common for close-in planets ($<0.1$ AU), especially those around M-type stars, because they are more X-ray luminous and thus enhancing photo-evaporation. The lessons we learn in this study may be helpful for the target selection of on-going/future exomoon searching programs.
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