To produce a highly pure argon product in a stable operation condition, by setting the theoretical number of stages of a crude argon tower so that the oxygen concentration of a liquified crude argon is within a range of a specified volume %, when extracting the liquified crude argon from the lower part of a deoxidation tower and leading it to the upper part of the crude argon tower.

The theoretical number of stages of a crude argon tower 5 is set so that the oxygen concentration of the top of the tower 5 is 0.3 vol.% or higher. That is, it is designed so that the deoxidation tower 7 bears the burden of a lower zone than 0.3 vol.% where the oxygen concentration is susceptible to disturbances. Accordingly, even when the flow rate of raw argon varies due to a disturbance, the fluctuation of the oxygen concentration in the crude argon tower 5 is small and disturbances are absorbed by a liquid reservoir 7a in the deoxidation tower 7. The theoretical number of stages of the crude argon tower 5 is set so that the oxygen concentration of the top of the crude argon tower 5 is no more than 2.5 vol.%, preferably no more than 2.0 vol.% to reduce the influence of disturbances to the utmost.