A beam-tracking simulation has been done for study of the electron- cooling bunching of ion beams around a few hundred MeV/u. In the simulation, the field due to the space charge of a beam in a round vacuum chamber is calculated from the charge distribution of macro- particles and the image particles due to the macro-particles. The simulation results show that the bunched beams meet a transverse instability more easily than coasting beams. (2 refs)