  We include the coupling of a heavy sterile neutrino with active neutrinos in
the calculation of primordial abundances of light-nuclei. We calculate neutrino
distribution functions and primordial abundances, as functions depending on a
renormalization of the sterile neutrino distribution function $(a)$, the
sterile neutrino mass $(m_s)$ and the mixing angle $(\phi)$. Using the
observable data, we set constrains on these parameters, which have the values
$a < 0.60$, $\sin^2 \phi=0.15$ and $m_s \approx 4$ keV, for a fixed value of
the baryon to photon ratio. When the baryon to photon ratio is allowed to vary,
its extracted value is in agreement with the values constrained by Planck
observations and by the Wilkinson Microwave Anisotropy Probe (WMAP). It is
found that the anomaly in the abundance of $^7$Li persists, in spite of the
inclusion of a heavy sterile neutrino.
