Based on the gauge symmetry group $SU(3)_Cotimes{SU(2)_L}otimes{U(1)_Y}otimes{U(1)_{B-L}}$, 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 $h^2Omega_{GW}sim10^{-11}$, which may be detectable in the future experiments.
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