  We demonstrate that Kerr/CFT duality can be extended to rotating charged
black hole solution surrounded by quintessence in Rastall gravity. Since
Rastall gravity can be considered as $F(R,T) = R + \beta T $ theory with the
addition of a matter term, so the gravitational Lagrangian is resemblant to
Einstein general relativity. In fact, the resulting central term is coincident
to the central term in the general relativity since $ T $ is only a trace of
the matter term. We then exhibit that the entropy from CFT of this black hole
is equivalent with the Bekenstein-Hawking entropy with no correction related to
the Rastall coupling constant. Moreover, when Rastall coupling constant $
\kappa \lambda $ is switched off and $ a $ is approaching zero, we may extend
the solution to the 5D black hole solution. It is found that this extremal
solution contains twofold CFT duals that we call as $Q$-picture and $ P
$-picture. In both pictures, the CFT entropy reproduces exactly the
Bekenstein-Hawking entropy for Reissner-Nordstr\"om black hole surrounded by
quintessence. The results establish that, for all black holes surrounded by
quintessence, the microscopic entropies of the dual CFTs agree with the
Bekenstein-Hawking entropies.
