  Many extensions of the Standard Model include a new $U(1)$ gauge group that
is broken spontaneously at a scale much above TeV. If a $U(1)$-breaking phase
transition occurs at nucleation temperature of $O(100)$-$O(1000)$~TeV, it can
generate stochastic gravitational waves in $O(10)$-$O(100)$ Hz range if
$\beta_{\rm n}/H_{\rm n}=1000$, which can be detected by ground-based
detectors. Meanwhile, supersymmetry (SUSY) may play a crucial role in the
dynamics of such high-scale $U(1)$ gauge symmetry breaking, because SUSY
breaking scale is expected to be at TeV to solve the hierarchy problem. In this
paper, we study the phase transition of $U(1)$ gauge symmetry breaking in a
SUSY model in the SUSY limit. We consider a particular example, the minimal
SUSY $U(1)_{B-L}$ model. We derive the finite temperature effective potential
of the model in the SUSY limit, study a $U(1)_{B-L}$-breaking phase transition,
and estimate gravitational waves generated from it.
