  We have studied the quasinormal modes (QNMs) of a slowly rotating black hole
with Lorentz-violating parameter in Einstein-bumblebee gravity. We analyse the
slow rotation approximation of the rotating black hole in the
Einstein-bumblebee gravity, and obtain the master equations for scalar
perturbation, vector perturbation and axial gravitational perturbation,
respectively. Using the matrix method and the continuous fraction method, we
numerically calculate the QNM frequencies. In particular, for scalar field, it
shows that the QNMs up to the second order of rotation parameter have higher
accuracy. The numerical results show that, for both scalar and vector fields,
the Lorentz-violating parameter has a significant effect on the imaginary part
of the QNM frequencies, while having a relatively smaller impact on the real
part of the QNM frequencies. But for axial gravitational perturbation, the
effect of increasing the Lorentz-violating parameter $\ell$ is similar to that
of increasing the rotation parameter $\tilde{a}$.
