Abstract: Collinear libration points of the restricted three-body problem with constant low thrust are studied. Varying the direction of the low thrust, the positions of the collinear libration points vary correspondingly. The set of the point L1 or L2 forms the shape of an elliptical “sphere” in space while the set of the point L3 forms the shape of a “banana”. The triangular libration points are also studied to show how they are connected with the collinear libration point L3. Concentrating on the points L1 and L2, linear solutions of the motions around them are obtained. Due to the asymmetry introduced by the low thrust, the linear solution has a form different from that of the unperturbed case. High order analytical solutions are also constructed. These solutions are compared with numerically integrated orbits. The comparison shows good agreement with each other. At last, periodic families around these two points are studied. These families include the planar and the vertical Lyapunov families, the halo family and another special periodic family. Bifurcation phenomena of these families are described.