  The Elementary Goldstone Higgs (EGH) model is a perturbative extension of the
standard model (SM), which identifies the EGH boson as the observed Higgs
boson. In this paper, we study pair production of the EGH boson in future
linear electron positron colliders. The cross sections in the TeV region can be
changed to about $-27\%$, $163\%$ and $-34\%$ for the $e^+e^-\rightarrow Zhh$,
$e^+e^-\rightarrow \nu\bar{\nu}hh$, and $e^+e^-\rightarrow t\bar{t}hh$
processes with respect to the SM predictions, respectively. According to the
expected measurement precisions, such correction effects might be observed in
future linear colliders. In addition, we compare the cross sections of double
SM-like Higgs boson production with the predictions in other new physics
models.
