The question "Can machines think?" and the Turing Test to assess whether machines could achieve human-level intelligence is one of the roots of AI. With the philosophical argument "I think, therefore I am", this paper challenge the idea of a "thinking machine" supported by current AIs since there is no sense of self in them. Current artificial intelligence is only seemingly intelligent information processing and does not truly understand or be subjectively aware of oneself and perceive the world with the self as human intelligence does. In this paper, we introduce a Brain-inspired and Self-based Artificial Intelligence (BriSe AI) paradigm. This BriSe AI paradigm is dedicated to coordinating various cognitive functions and learning strategies in a self-organized manner to build human-level AI models and robotic applications. Specifically, BriSe AI emphasizes the crucial role of the Self in shaping the future AI, rooted with a practical hierarchical Self framework, including Perception and Learning, Bodily Self, Autonomous Self, Social Self, and Conceptual Self. The hierarchical framework of the Self highlights self-based environment perception, self-bodily modeling, autonomous interaction with the environment, social interaction and collaboration with others, and even more abstract understanding of the Self. Furthermore, the positive mutual promotion and support among multiple levels of Self, as well as between Self and learning, enhance the BriSe AI's conscious understanding of information and flexible adaptation to complex environments, serving as a driving force propelling BriSe AI towards real Artificial General Intelligence.