Abstract: Orbital dynamics with solar gravity perturbation in the vicinity of the irregular asteroids is studied in this paper. The motions in the gravity fields of 216 HIeopatra and 433 Eros , and the periodic orbits around the asteroids with perturbation of solar gravitation are analyzed to find a new family of periodic orbits of 216 HIeopatra. It is also found that there are 12 families of periodic orbits as well as a bounded non-periodic orbit around 433 Eros , and their topology and stability are studied in some details. The results show that solar gravitation has little effects on the positions of asteroids equilibria in the body-fixed frame while has greater effects on the motions of a spacecraft on the equilibria. The solar gravitation is not strong enough to increase or decrease the families of periodic orbits, nor is it able to change the stabilities of periodic orbits. It is easier for orbits with larger Jacobi constant to keep their periodic characteristics under the solar perturbation that gave a new thread to explain why asteroids can have some satellites in far distance for a long time.