Theory of mind (ToM) refers to humans' ability to understand and infer the desires, beliefs, and intentions of others. The acquisition of ToM plays a key role in humans' social cognition and interpersonal relations. Though indispensable for social intelligence, ToM is still lacking for modern AI and NLP systems since they cannot access the human mental state and cognitive process beneath the training corpus. To empower AI systems with the ToM ability and narrow the gap between them and humans, in this paper, we propose COKE: the first cognitive knowledge graph for machine theory of mind. Specifically, COKE formalizes ToM as a collection of 45k+ manually verified cognitive chains that characterize human mental activities and subsequent behavioral/affective responses when facing specific social circumstances. Beyond that, we further generalize COKE using pre-trained language models and build a powerful cognitive generation model COKE+. Experimental results in both automatic and human evaluation demonstrate the high quality of COKE and the superior ToM ability of COKE+.