Abstract : The equivalent two-body method [H. Feshbach and S. I. Rubinow, Phys. Rev. 98, 188 (1955)] has been applied to investigate the weakly bound states of a three-body system. An analytical expression for the long-range effective potential is derived if two-body interactions are short-range potentials with Yukawa forms. The weakly bound excited state for the system with two heavy particles and a light particle is first obtained if there is no bound state for two-body subsystems.