•Tax-based pure punishment has an evolutionary advantage over pure punishment in sustaining cooperation.•Tax-based pure reward has an evolutionary advantage over pure reward in sustaining cooperation.•Tax-based pure reward can lead to higher levels of cooperation when it is compared with tax-based pure punishment. Costly punishment and reward have been regarded as potential means to handle the conundrum of cooperation. However, providing incentives is costly, thus the emergence of costly punishment and reward is a major puzzle in the evolution of cooperation. Recently, it is found that pure punishers, who do not help others but punish free-riders, have an evolutionary advantage. In this work, based on the pure punishment strategy, we further propose tax-based pure punishment and reward strategies in the public goods game respectively by considering that in realistic world the dedicated sanctioning or rewarding agencies can receive a certain amount of revenue tax to penalize evildoers or reward good men. By means of theoretical analysis and numerical calculations, we find that tax-based pure punishment (reward) has an evolutionary advantage over pure punishment (reward) in sustaining cooperation, and tax-based pure reward can lead to higher level of cooperation than tax-based pure punishment.