This work presents some preliminary results on the low-thrust tour of the main asteroid belt. The asteroids are visited through a series of fly-by’s that minimise the total cost of the manoeuvres. The sequence of asteroids to visit and the initial orbit for the spacecraft are chosen based on the Minimum Orbit Intersection Distance (MOID) between the orbit of the asteroids and the orbit of the spacecraft. The transfers between asteroids are designed using a low-thrust analytical model that provides nearly optimal solutions with coast and thrust arcs. The mission analysis is completed with a study of the transfer of the spacecraft from the Earth to the first orbit of the tour.