Cognitive-functional dialogues, such as those for persuasion, consultation, and question-answering, are prevalent throughout human social interaction. The core difference between these dialogues and casual chat lies in their objective: to guide a person's cognitive and psychological state toward a predetermined one. Existing conversational technologies perform poorly in handling such dialogues. The fundamental reason is that the transformation of human cognitive psychology follows specific patterns, yet existing technologies neither account for these patterns nor possess cognitive guidance planning based on them. This deficiency makes it difficult for dialogues to achieve their intended cognitive-functional goals effectively. To address this, we propose a dynamic cognitive planning method (DyCoP). By modeling the long-term evolution of a user's cognitive psychology during the dialogue process, this method dynamically generates dialogue guidance plans that align with the principles of cognitive-psychological evolution. This allows for the generation of appropriate dialogue responses based on prior user psychology and the immediate conversational context, thereby achieving cognitive-functional goals more efficiently and accurately. Simultaneously, we constructed an evaluation framework for cognitive-functional dialogues and constructed a richly annotated emotional support conversation dataset. Comprehensive automatic and human evaluations show that our proposed DyCoP method demonstrates significant advantages over existing baseline models.