An additional (U\left(1\right)) gauge interaction is one of the promising extensions of the standard model of particle physics. Among others, the (U\left(1{\right)}{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\left(1{\right)}{B-L}) model, the symmetry breaking of the extra (U\left(1\right)) 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 that is detectable in future experiments.