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The lunar probe often has some remaining fuel on completing the predefined Moon exploration mission and may carry out some additional tasks from the Moon orbit using the fuel. The possibility for the lunar probe to escape from the Moon and the Earth is analyzed. Design and optimization of the trajectory from the Moon orbit to the Near Earth Asteroids （NEAs） using the spacecraft＇s residual fuel is studied. At first, the semi-major axis, inclinations and the phase relations with the Earth of all the numbered NEAs are investigated to preliminarily select the possible targets. Based on the Sun-centered two-body problem, the launch window and the asteroid candidates are determined by calculating the minimum delta-v for two-impulse rendezvous mission and one-impulse flyby mission, respectively. For a precise designed trajectory, a full ephemeris dynamical model, which includes gravities of the Sun, the planets and the Moon, is adopted by reading the JPL ephemeris. The departure time, arrival time, burning time duration and thrust angles are set as variables to be designed and optimized. The optimization problem is solved via the Particle Swarm Optimization （PSO） algorithm. Moreover, two feasible NEA flyby missions are presented.