A three-dimension elliptic restricted three-body model for the gravity-assist technology in interplanetary exploration was developed based on the planar elliptic restricted three-body model by introducing two extra parameters. By using integrated backward and integrated forward method, the energies and angular momentums of the spacecraft before and after the gravity-assist were obtained. Thus, the orbits can be divided into sixteen different types. The influences of the two extra parameters on the orbit of spacecraft were discussed and the variation laws were summarized. With the Earth-Moon system as an example, the selection region of gravity-assist parameters that can achieve escape and captive was calculated. In addition, the gravity-assist parameters were optimized.