There are observational evidences for the existence of twisted magnetic field in the solar corona. This inspires us to investigate the effect of a twisted magnetic field on the evolution of magnetohydrodynamic (MHD) kink waves in coronal loops. To this aim, we solve the incompressible linearized MHD equations in a magnetically twisted non-uniform coronal flux tube in the limit of long wavelengths. Our results show that a twisted magnetic field can enhance or diminish the rate of phase-mixing of the Alfven continuum modes and the decay rate of the global kink oscillation. Also our results confirm that in the presence of a twisted magnetic field, the quasi-mode frequency of the kink waves is asymmetric with respect to the propagation direction. Even a small amount of twist can have an important impact on the process of energy cascade to small scales.
