This paper studies the energy based control of an underactuated two-link robot called the Pendubot. After having investigated the characteristics of the closed-loop systems with the energy based control law in Fantoni et al. (IEEE-AC’2000) for swinging the Pendubot up, this paper proposes a sufficient condition about parameters in the control law such that the total energy of the Pendubot will converge to the potential energy of its top upright position. This paper gives an answer to the unsolved issue in Fantoni et al. (IEEE-AC’2000) whether the total energy of the Pendubot will converge to the potential energy of its top upright position. Moreover, with the aid of the proposed condition, the parameters in the control law are easy to be chosen.