By assuming the existence of extra-dimensional sterile neutrinos in big bang nucleosynthesis (BBN) epoch, we investigate the sterile neutrino ($ u_{rm s}$) effects on the BBN and constrain some parameters associated with the $ u_{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 $ u_{rm s}$ traveling on or off the brane are considered. In this model, the effective mixing angle between a $ u_{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 $ u_{rm s}$ can be drastically changed during the cosmic evolution. We estimated abundances and temperature of the $ u_{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 $ u_{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 $ u_{rm s}$, mixing angle and mass difference, are discussed in detail with the comparison of our BBN calculations corrected by the extra-dimensional $ u_{rm s}$ to observational data on light element abundances.
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