  We obtain an exact Kerr-like black hole solution by solving the corresponding
gravitational field equations in Einstein-bumblebee gravity model where Lorentz
symmetry is spontaneously broken once a vector field acquires a vacuum
expectation value. Results are presented for the purely radial Lorentz symmetry
breaking. In order to study the effects of this breaking, we consider the black
hole shadow and find that the radial of the unstable spherical orbit on the
equatorial plane $r_c$ decreases with the Lorentz breaking constant $\ell>0$,
and increases with $\ell<0$. These shifts are similar to those of
Einstein-aether black hole. The effect of the LV parameter on the black hole
shadow is that it accelerates the appearance of shadow distortion, and could be
detected by the new generation of gravitational antennas.
