Gravitational capture is a mechanism by which an object from outside the sphere of influence can orbit around a celestial body temporarily, without any other effects such as atmospheric drag. In this paper, gravitational capture conditions are extensively sought laying emphasis on lunar capture portion using backward time integration mainly in the earth-moon-S/C three-body system. Perilune velocity band satisfying the gravitational capture conditions is found to be constituted of three sub-bands mainly corresponding to its capture direction in the earth-moon fixed rotating frame. An analysis of geocentric orbit with solar effect linking the earth and lunar gravitational capture orbit is also performed for construction of earth-moon transfer orbit. Transfer orbits of various types are designed in the sun-earth-moon-S/C four-body system, which indicate the feasibility of gravitational capture with reasonable ΔV and flight time.