As AI closely interacts with human society, it is crucial to ensure that its decision-making is safe, altruistic, and aligned with human ethical and moral values. However, existing research on embedding ethical and moral considerations into AI remains insufficient, and previous external constraints based on principles and rules are inadequate to provide AI with long-term stability and generalization capabilities. In contrast, the intrinsic altruistic motivation based on empathy is more willing, spontaneous, and robust. Therefore, this paper is dedicated to autonomously driving intelligent agents to acquire morally behaviors through human-like affective empathy mechanisms. We draw inspiration from the neural mechanism of human brain's moral intuitive decision-making, and simulate the mirror neuron system to construct a brain-inspired affective empathy-driven altruistic decision-making model. Here, empathy directly impacts dopamine release to form intrinsic altruistic motivation. Based on the principle of moral utilitarianism, we design the moral reward function that integrates intrinsic empathy and extrinsic self-task goals. A comprehensive experimental scenario incorporating empathetic processes, personal objectives, and altruistic goals is developed. The proposed model enables the agent to make consistent moral decisions (prioritizing altruism) by balancing self-interest with the well-being of others. We further introduce inhibitory neurons to regulate different levels of empathy and verify the positive correlation between empathy levels and altruistic preferences, yielding conclusions consistent with findings from psychological behavioral experiments. This work provides a feasible solution for the development of ethical AI by leveraging the intrinsic human-like empathy mechanisms, and contributes to the harmonious coexistence between humans and AI.