The author analyses ion-cyclotron instability of oscillations in a plasma cylinder in which cold magnetized electrons perform Langmuir oscillations in the magnetic field direction while the ions (with an anisotropic velocity distribution) oscillate across the magnetic field. Dispersion equations are obtained for waves rotating in the direction of ion rotation and in the opposite direction. It is shown that the wave build-up is most intense in waves propagated in the direction of ion rotation.