  We compute the cosmological boost factor at high redshifts of $z=10$-$100$ by
integrating the non-linear matter power spectrum measured from high-resolution
cosmological $N$-body simulations. An accurate boost factor is required to
estimate the energy injection from dark matter annihilation, which may affect
the cosmological re-ionization process. We combined various box-size
simulations (side lengths of $1 \, {\rm kpc}$-$10 \, {\rm Mpc}$) to cover a
wide range of scales, i.e. $k=1$-$10^7 \, {\rm Mpc}^{-1}$. The boost factor is
consistent with the linear theory prediction at $z \gtrsim 50$ but strongly
enhanced at $z \lesssim 40$ as a result of non-linear matter clustering.
Although dark matter free-streaming damping was imposed at $k_{\rm fs}=10^6 \,
{\rm Mpc}^{-1}$ in the initial power spectrum, the damping disappears at later
times of $z\lesssim40$ as a result of the power transfer from large to small
scales. Because the simulations do not explore very small-scale clustering at
$k>10^7 \, {\rm Mpc}^{-1}$, our result is a lower bound on the boost factor at
$z \lesssim 40$. A simple fitting function of the boost factor is also
presented.
