The isothermal initial oxidation kinetics of Zr55Cu30Al10Ni5 bulk metallic glass in glassy state (lower than Tg = 685K) and in surpercooled liquid state (Tg = 685 K < T < Tx=774 K) is investigated under dry air by thermogravimetric method in short-term stage (for 1.5 hours). A protective parabolic law is followed in glassy state, except at 573 K where a linear law is followed. The self-limiting oxidation kinetics evolves from a short linear stage to a steady mild growth stage in supercooled liquid state at 723 K, which is induced mainly by crystallization and by the fast growth of dense scale. The growth of the scale is dominated by the formation of tetragonal-ZrO2 (t- ZrO2) in the range of 623 K - 673 K in glassy state for 1.5 hours. The activation energy of oxidation is mainly piloted by the diffusion of oxygen ions.