Abstract: Altruistic punishment, which occurs when an individual incurs a cost to punish unfairness or norm violation, may play a role in perpetuating cooperation. The neural mechanism underlying costly punishment has only recently begun to be explored. Here we review current studies on the neural basis of altruism from the perspectives of costly punishment, emphasizing the importance of elementary neural processes underlying a decision to punish. Particularly,there are four cognitive processes that contribute to the decision to altruistically punish in most situations: inequity aversion, cost-benefit calculation, social reference frame to distinguish self from others and cognitive control. Overall, understanding the neural mechanism of altruistic punishment with respect to the core computations necessary to achieve a decision to punish is useful for us to learn the altruistic behavior of human being.