  We study the "topological gauged WZW model associated with
$SU(2)/U(1)$",which is defined as the twisted version of the corresponding
supersymmetric gauged WZW model. It is shown that this model is equivalent to a
topological conformal field theory characterized by two independent topological
conformal algebras, one of which is the "twisted Kazama-Suzuki type" and the
other is "twisted Coulomb gas type". We further show that our formalism of this
gauged WZW model naturally reduces to the well-known formulations of 2D gravity
coupled with conformal matter; one of the gauge choices leads to the K.Li's
theory, and the alternative choices lead to the KPZ theory or the DDK
(Liouville) theory.
