Power restriction is the basic premise to prevent power abuse, and power supervision is the basic form of power restriction. As socialism with Chinese characteristics has entered a New Era, standing at the height of history and times, the communist party of China has carried out new thoughts and explorations on why and how to strengthen power supervision. It is necessary to deepen ideological understanding and clarify the logic of strengthening power supervision in the new era from the aspects of the nature of power which lies in the people, the duality of power operation and the importance of power function; to make clear the supervision path, and establish a comprehensive, goal oriented, authoritative and efficient power supervision system；to adhere to multiple measures, build an ideological and moral defense line with party spirit education, a rigid normative system with laws and regulations, a power constraint system with democratic rights, and optimize the power operation mechanism with power allocation so as to explore a way of power supervision with Chinese characteristics.