We present results for the light quark masses for the Wilson quark action obtained with the PCAC relation for the one-link extended axial vector current in quenched QCD at beta = 5.9-6.5. This method leads to a remarkable improvement of scaling behavior of the light quark masses compared to the conventional method. We obtain (m) over bar(t) = 3.87(37)MeV for the averaged up and down quark mass and (m) over bar(s) = 97(9)MeV for the strange quark mass in the <(MS)over bar> scheme at mu = 2GeV.