In this paper, the formation of small asteroids which are categolized as a Rubble Pile asteroid, having an elongated body, is studied. Itokawa, a typical Near Earth Asteroid (NEA), is a good example. As for these asteroids, it is considered that after the collapse of the preexisting parent body, the fragments reaggregate to an asteroid. This paper discusses this formation by dividing into two formation processes. In the first process, large fragments just after the preexisting parent asterod collapsing grow up to a dumbbell-shaped body by aggregation of the fragments. In the second, mass free fragments orbit around the core body and some of them accrete to the core body. In this paper, at first, we specify the second process because of its simplicity. In the beginning, the linear stability around the core body is shown. The dumbbell-shape body is modeled by two sphere-shaped bodies with a rigid and mass free stick. Then, the motion of mass-free fragments around the dumbbell-shaped body is shown by numerical calculations. Moreover, the mass ratio and the angular velocity ratio between a primary dumbbell-shaped body and a current elongated body is estimated. Next, the first process is shown by numerical analysis of the motion of large fragments. In this process, the multi-body problem is utilized. From these analysis, we find the following subjects. In second process, there are three stable points around the dumbbell-shaped body. The motion of fragments is characterized by Hill's sphere. The fragments inside Hill's sphere accrete to the dumbbell-shaped body. On the other hand, while most fragments outside Hill's sphere move away from the dumbbell-shaped body, some of them enter into Hill's sphere and attach accrete to it, passing through saddle points. Then, the analysis of the relation of the current body and the primary body indicates that when the mass ratio of the current body and the primary body is small, if fragments around the primary body do not have a part of the angular momentum, the total angular momentum is no longer conserved. In the first process, the numerical analysis show that the size of the total mass and the density of dust nebula. The primary condition affects the number of asteroids in the end.