  We have studied quasi-periodic oscillations frequencies in a rotating black
hole with Lorentz symmetry breaking parameter in Einstein-bumblebee gravity by
relativistic precession model. We find that in the rotating case with non-zero
spin parameter both of the periastron and nodal precession frequencies increase
with the Lorentz symmetry breaking parameter, but the azimuthal frequency
decreases. In the non-rotating black hole case, the nodal precession frequency
disappears for arbitrary Lorentz symmetry breaking parameter. With the
observation data of GRO J1655-40, XTE J1550-564, and GRS 1915+105, we find that
the constraint on the Lorentz symmetry breaking parameter is more precise with
data of GRO J1655-40 in which the best-fit value of the Lorentz symmetry
breaking parameter is negative. This could lead to that the rotating black hole
in Einstein-bumblebee gravity owns the higher Hawking temperature and the
stronger Hawking radiation, but the lower possibility of exacting energy by
Penrose process. However, in the range of $1 \sigma$, we also find that general
relativity remains to be consistent with the observation data of GRO J1655-40,
XTE J1550-564 and GRS 1915+105.
