  One of the problems in the current context of asymptotic symmetry is to
extend the black hole considered to the rotating one. Therefore, we in this
paper obtain a four-dimensional asymptotically flat rotating black hole
solution including the displacement of supertraslation. Since it has been
obtained not by solving Einstein equation but based on the already obtained
supertranslated Schwarzschild black hole solution by using coordinate
transformations, it is not the general solution. However, it is sure that it is
`a' supertranslated rotating black hole solution as it can satisfy the Einstein
equation. Then, as one of the interesting issues on the supertranslated
rotating black hole, we analyze the classical gravitational perturbation with
the effect of the rotating black hole by expanding with regard to $r$ from the
infinity to the order where the effect of the rotation of the black hole can
finally remain in the result.
