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This paper demonstrates that an adjustment process of the global carbon tax rate can be chaotic. To this end, a discrete-time dynamic game is constructed in which the environmental regulator updates the tax rate for given observation of the regulated industry's CO2 emissions. It is shown that if the regulator considers the marginal benefit of increasing the tax rate is high, the adjustment process becomes chaotic. It is also demonstrated that the atmospheric CO2 concentration level with chaotic emission is higher than the level with a stationary state of "high tax and low emissions." Given that the regulator wishes to control the concentration level with low emission, an adaptive adjustment of the tax rate is investigated.

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