  The $U(1)_{B-L}$ gauge symmetry is a promising extension of the standard
model of particle physics, which is supposed to be broken at some high energy
scale. Associated with the $U(1)_{B-L}$ gauge symmetry breaking, right-handed
neutrinos acquire their Majorana masses and then tiny light neutrino masses are
generated through the seesaw mechanism. In this paper, we demonstrate that the
first-order phase transition of the $U(1)_{B-L}$ gauge symmetry breaking can
generate a large amplitude of stochastic gravitational wave (GW) radiation for
some parameter space of the model, which is detectable in future experiments.
Therefore, the detection of GWs is an interesting strategy to probe the seesaw
scale which can be much higher than the energy scale of collider experiments.
