  We consider models with a noncompact symmetry in the framework of
$\mathcal{N}=1$ supersymmetry. Contrary to the conventional approach, the
noncompact symmetry is realized linearly on all fields without constraints. The
models are constructed using noncanonical K\"ahler function and gauge kinetic
function, which is introduced for the local case. It is explained that the
symmetry needs to be spontaneously broken for the consistency of a model. We
study the vacuum structures of two models with the noncompact symmetry SU(1,1)
for both global and local cases. One of them includes two fundamental
representations of the group and the other includes one adjoint representation.
It is shown that the former is consistent for the global case and the latter is
consistent for both the global and local cases.
