Abstract: The transverse vibration of a tethered satellite is studied. The equation of thevibration is formulated. To suppress the transverse vibration of the tethered satellite, the longitudinal control force is gotten by Pontryagin's method. The controlforce to exert to the tether is produced by D'Alembert force of satellites, and satellites are accelerated by the change of the tether's length, which is controlled by themotor in the satellite. The numerical simulation results are included.