We are interested in stable periodic orbits for spacecraft in the gravitational field of minor celestial bodies. The stable periodic orbits around minor celestial bodies are useful not only for the mission design of the deep space exploration, but also for studying the long-time stability of small satellites in the large-size-ratio binary asteroids. The irregular shapes and gravitational fields of the minor celestial bodies are modeled by the polyhedral model. Using the topological classifications of periodic orbits and the grid search method, the stable periodic orbits can be calculated and the topological cases can be determined. Furthermore, we find five different types of stable periodic orbits around minor celestial bodies: (1) stable periodic orbits generated from the stable equilibrium points outside the minor celestial body; (2) stable periodic orbits continued from the unstable periodic orbits around the unstable equilibrium points; (3) retrograde and nearly circular periodic orbits with zeroinclination around minor celestial bodies; (4) resonance periodic orbits; (5) near-surface inclined periodic orbits. We take asteroids 243 Ida, 433 Eros, 6489 Golevka, 101955 Bennu, and the comet 1P/Halley for examples.