  Higgs boson production associated with a top quark pair is an important
process in studying the nature of the newly discovered Higgs boson at the LHC.
In this letter, we report on our calculations including the next-to-leading
order (NLO) QCD and NLO electroweak corrections to the $pp\to t\bar{t}H$
process in the standard model. We present the integrated cross sections at the
$14~{\rm TeV}$ LHC and even at the future proton-proton colliders with
$\sqrt{s}=33$ and $100~{\rm TeV}$. Our calculation includes the top quark
subsequent decays by adopting the narrow width approximation. The kinematic
distributions of Higgs boson and top quark decay products at the LHC are
provided. We find that the ${\cal O}(\alpha_s^2\alpha_{ew}^2)$ corrections are
quantitatively comparable with the ${\cal O}(\alpha_s^3\alpha_{ew})$
corrections in some kinematic region.
