  We study the Higgs pair-production in the Standard Model of the strong and
electroweak interactions at future $e^{+}e^{-}$ collider energies, with the
reaction $e^{+}e^{-}\to t \bar t HH$. We evaluated the total cross section of
$t\bar tHH$ and calculate the number total of events considering the complete
set of Feynman diagrams at tree-level. The numerical computation is done for
the energy which is expected to be available at a possible Next Linear
$e^{+}e^{-}$ Collider: with center-of-mass energy $800, 1600$ $GeV$ and
luminosity 1000 $fb^{-1}$.
