  Based on the gauge symmetry group
$SU(3)_C\otimes{SU(2)_L}\otimes{U(1)_Y}\otimes{U(1)_{B-L}}$, the minimal
supersymmetric extension of the SM with local B-L gauge symmetry(B-LSSM) has
been introduced. In this model, we study the Higgs masses with the one-loop
zero temperature effective potential corrections. Besides, the finite
temperature effective potentials connected with two $U(1)_{B-L}$ Higgs singlets
are deduced specifically. Then we can obtain the gravitational wave spectrums
generated from the strong first-order phase transition. In the B-LSSM, the
gravitational wave signals can be as strong as $h^2\Omega_{GW}\sim10^{-11}$,
which may be detectable in the future experiments.
