  Assuming the existence of an eV or KeV scale sterile neutrino, we develop a
3+1 neutrino mass model using $A_4\times Z_4 \times Z_2$ symmetry group. Three
Higgs $H, H^{\prime}$ and $H^{\prime\prime}$ are considered to give a desired
neutrino mass matrix which generates non-zero $\theta_{13}$. The model can give
neutrino mixing parameters that are well within the experimental 3$\sigma$
bounds. We also calculate the $4\times 4$ active-sterile neutrino mixing
matrix, and it is found to be consistent with experimental bounds.
