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We study the phenomenology of the light and heavy Higgs boson production anddecay in the context of a $U(1)_{B-L}$ extension of the Standard Model with anadditional $Z'$ boson at future $e^+e^-$ linear colliders with center-of-massenergies of $\sqrt{s}=500-3000\hspace{0.8mm}GeV$ and integrated luminosities of${\cal L}=500-2000\hspace{0.8mm}fb^{-1}$. The study includes the processes$e^{+}e^{-}\rightarrow (Z, Z') \to Zh$ and $e^{+}e^{-}\rightarrow (Z, Z') \toZH$, considering both the resonant and non-resonant effects. We find that thetotal number of expected $Zh$ and $ZH$ events can reach 909,124 and 97,487,respectively, which is a very optimistic scenario and thus it would be possibleto perform precision measurements for both Higgs bosons $h$ and $H$, as well asfor the $Z'$ boson in future high-energy and high-luminosity $e^+e^-$ collidersexperiments. Our study complements other studies on the B-L model and on theHiggs-strahlung processes $e^{+}e^{-}\rightarrow (Z, Z') \to Zh$ and$e^{+}e^{-}\rightarrow (Z, Z') \to ZH$.

Higgs bosons production and decay at future $e^+e^-$ linear colliders as a probe of the B-L model