  In the framework of the minimal $U(1)_{B-L}$ extension of the Standard Model,
we investigate the Higgs boson production processes $e^{+}e^{-}\rightarrow ZH$,
$e^{+}e^{-}\rightarrow \nu_{e}\bar{\nu_{e}}H$, $e^{+}e^{-}\rightarrow
t\bar{t}H$, $e^{+}e^{-}\rightarrow ZHH$ and $e^{+}e^{-}\rightarrow
\nu_{e}\bar{\nu_{e}}HH$ at the International Linear Collider (ILC). We present
the production cross sections, the relative corrections and compare our results
with the expected experimental accuracies for Higgs decay channel $H\rightarrow
b\bar{b}$. In the allowed parameter space, we find that the effects of the
three single Higgs boson production processes might approach the observable
threshold of the ILC, and that the Higgs signal strengths $\mu_{b\bar{b}}$ of
the two double Higgs boson production processes are all out of the observable
threshold of the ILC so that the effects will be difficult to be observed at
the ILC.
