  An additional $U(1)$ gauge interaction is one of promising extensions of the
standard model of particle physics. Among others, the $U(1)_{B-L}$ gauge
symmetry is particularly interesting because it addresses the origin of
Majorana masses of right-handed neutrinos, which naturally leads to tiny light
neutrino masses through the seesaw mechanism. We show that, based on the
minimal $U(1)_{B-L}$ model, the symmetry breaking of the extra $U(1)$ gauge
symmetry with its minimal Higgs sector in the early Universe can exhibit the
first-order phase transition and hence generate a large enough amplitude of
stochastic gravitational wave radiation which is detectable in future
experiments.
