We investigate Cerenkov electron absorption of low-frequency electromagnetic waves in an inhomogeneous plasma cylinder. Formulas were obtained for the energy absorbed by plasma, and for the damping factor where there is no resonance layer. A sharp boundary leads to a strong absorption increase. For a resonance layer containing a point at which the radial wave number becomes infinite, there occurs a strong absorption increase (if the phase velocity of the wave is the order of thermal-electron velocity, then the damping rate is the same order as the frequency). The radial and axial components of the electric field of the wave then increase sharply in the resonance layer. The increase in absorption is caused by the axial component of the electric field. Formulas were derived for the electric field strength inside the resonance layer, for the high-frequency power that is absorbed by the layer; and for the width of the layer.