  We investigate effects of cosmic-rays on the linear growth of the
Kelvin-Helmholtz instability. Cosmic-rays are treated as an adiabatic gas and
allowed to diffuse along magnetic field lines. We calculated the dispersion
relation of the instability for various sets of two free parameters, the ratio
of the cosmic-ray pressure to the thermal gas pressure and the diffusion
coefficient. Including cosmic-ray effects, a shear layer is more destabilized
and the growth rates can be enhanced in comparison with the ideal
magnetohydrodynamical case. Whether the growth rate is effectively enhanced or
not depends on the diffusion coefficient of cosmic-rays. We obtain the
criterion for effective enhancement by comparing the growing time scale of the
instability with the diffusion time scale of cosmic-rays. These results can be
applied to various astrophysical phenomena where a velocity shear is present,
such as outflows from star-forming galaxies, AGN jet, channel flows resulting
from the nonlinear development of the magnetorotational instability, and
galactic disks.
