We propose a B - L model combined with the S-4 x Z(3) x Z(4) discrete symmetry that successfully explains the recent 3+1 sterile-active neutrino data. The smallness of the neutrino mass is obtained through the type-I seesaw mechanism. The active active and sterile-active neutrino mixing angles are predicted to be consistent with the recent constraints in which 0.3401 (0.3402) <= sin(2) theta(12) <= 0.3415 (0.3416), 0.456 (0.433) <= sin(2) theta(23) <= 0.544 (0.545), 2.00 (2.018) <= 10(2) x sin(2) theta(13) <= 2.405 (2.424), 156 (140.8) <= delta((circle))(CP) <= 172 (167.2) for normal (inverted) ordering of the three-neutrino scenario, and 0.015 (0.022) <= s(14)(2) 0.045 (0.029), 0.005(0.0095) <= s(24)(2 )<= 0.012 (0.012), 0.003 (0.009) <= s(34)(2) <= 0.011 for normal (inverted) ordering of the 3+1 neutrino scenario. Our model predicts flavor-conserving leptonic neutral scalar interactions and successfully explains the muon g - 2 anomaly.