The strange quark mass is calculated from QCD sum rules for the divergence of the vector as well as axial-vector current in the next-next-to-leading logarithmic approximation. The determination for the divergence of the axial-vector current is found to be unreliable due to large uncertainties in the hadronic parametrisation of the two-point function.From the sum rule for the divergence of the vector current, we obtain a value of m s ≡ m s (1 GeV) = 189 ± 32 MeV, where the error is dominated by the unknown perturbative O(α 3 s ) correction. Assuming a continued geometric growth of the perturbation series, we find m s = 178 ± 18 MeV. Using both determinations of m s , together with quark-mass ratios from chiral perturbation theory, we also give estimates of the light quark masses m u and m d .