The recent detection of gravitational wave signal from binary
compact star merger has set a strong constraint on tidal defomability,
which motivated a large amount of studies about the equation of state.
But the tidal deformability of compact star depends not only on the
equation of state, but also on the spin and magnetic field of the star.
In this study, we calculated for the first time the contribution of
tidal deformability from magnetic field. Both the magnetic field and
tidal field act as a perturbation of a spherical star. We found that
they are independent with each other at first order because of linearity
of perturbed equations, and their coupling firstly appears in the second
order of perturbation. Our results show that the correction of tidal
deformability is only about 0.1% for magnetic field at surface of star
is 10^15 gauss. We explored the difference of our results from neutron
star and quark star. the possibility of detection for this difference
from magnetic field in the future gravitational wave observations are