There are ample evidences of twisted magnetic structures in the solar corona. This motivates us to consider the magnetic twist as the cause of Alfven frequency continuum in the coronal loops, which can support the resonant absorption as a rapid damping mechanism for the observed coronal kink magnetohydrodynamic (MHD) oscillations. In the thin tube thin boundary approximations we derive the dispersion relation and solve it analytically to obtain the frequencies and damping rates of the fundamental (l=1) kink (m=1) MHD mode. We conclude that the resonant absorption by the magnetic twist can justify the rapid damping of kink MHD waves observed in coronal loops. Furthermore, the magnetic twist in the inhomogeneous layer can cause deviations from P1/P2=2 which are comparable with the observations.
