We construct a multiscalar and nonrenormalizable $B-L$ model with $A_4times Z_3times Z_4$ flavor symmetry which successfully explains the recent $3+1$ active-sterile neutrino data. The tiny neutrino mass the mass hierarchy are obtained by the type-I seesaw mechanism. The hierarchy of the lepton masses is satisfied by a factor of $v_H left(frac{v_l}{Lambda}right)^2 sim 10^{-4}, mathrm{GeV}$ of the electron mass compared to the muon and tau masses of the order of $frac{v_H v_l}{Lambda} sim 10^{-1}, mathrm{GeV}$. The recent $3+1$ active-sterile neutrino mixings are predicted to be $0.015 leq|U_{e 4}|^2leq 0.045$, $0.004 leq|U_{mu 4}|^2leq 0.012$, $0.004 leq|U_{tau 4}|^2leq 0.014$ for normal hierarchy and $0.020leq|U_{e 4}|^2leq 0.045$, $0.008 leq|U_{mu 4}|^2leq 0.018$, $0.008leq|U_{tau 4}|^2leq 0.022$ for inverted hierarchy. Sterile neutrino masses are predicted to be $0.7 lesssim m_s , (mathrm{eV}) lesssim 3.16$ for normal hierarchy and $2.6 lesssim m_s , (mathrm{eV}) lesssim 7.1$ for inverted hierarchy. For three neutrino scheme the model predicts $0.3401 leq sin^2theta_{12}leq 0.3415, , 0.460 leq sin^2theta_{23}leq 0.540,, -0.60 leq sindelta_{CP}leq -0.20$ for normal hierarchy and $0.3402 leq sin^2theta_{12}leq 0.3416,, 0.434leqsin^2theta_{23}leq 0.610,, -0.95 leq sindelta_{CP}leq -0.60$ for inverted hierarchy. The effective neutrino masses are predicted to be $35.70 leq langle m_{ee}rangle [mbox{meV}] leq 36.50$ in 3+1 scheme and $3.65 leq langle m^{(3)}_{ee}rangle [mbox{meV}] leq 4.10$ in three neutrino scheme for NH while $160.0 leq langle m_{ee}rangle [mbox{meV}] leq 168.0$ in 3+1 scheme and $47.80 leq langle m^{(3)}_{ee}rangle [mbox{meV}] leq 48.70$ in three neutrino scheme for for IH which are all in agreement with the recent experimental data.
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