  By assuming the existence of extra-dimensional sterile neutrinos in big bang
nucleosynthesis (BBN) epoch, we investigate the sterile neutrino ($\nu_{\rm
s}$) effects on the BBN and constrain some parameters associated with the
$\nu_{\rm s}$ properties. First, for cosmic expansion rate, we take into
account effects of a five-dimensional bulk and intrinsic tension of the brane
embedded in the bulk, and constrain a key parameter of the extra dimension by
using the observational element abundances. Second, effects of the $\nu_{\rm
s}$ traveling on or off the brane are considered. In this model, the effective
mixing angle between a $\nu_{\rm s}$ and an active neutrino depends on energy,
which may give rise to a resonance effect on the mixing angle. Consequently,
reaction rate of the $\nu_{\rm s}$ can be drastically changed during the cosmic
evolution. We estimated abundances and temperature of the $\nu_{\rm s}$ by
solving the rate equation as a function of temperature until the sterile
neutrino decoupling. We then find that the relic abundance of the $\nu_{\rm s}$
is drastically enhanced by the extra-dimension and maximized for a
characteristic resonance energy $E_{\rm res}\gtrsim 0.01$ GeV. Finally, some
constraints related to the $\nu_{\rm s}$, mixing angle and mass difference, are
discussed in detail with the comparison of our BBN calculations corrected by
the extra-dimensional $\nu_{\rm s}$ to observational data on light element
abundances.
