Large Language Models (LLMs) have demonstrated strong performance in open-ended generation tasks. However, they often struggle to adapt content to users with differing cognitive capacities, leading to a phenomenon we term cognitive misalignment. This issue arises in two forms: knowledge-level misalignment, where content is too complex or too simplistic relative to user understanding, and presentation-style misalignment, where the structure or tone hinders effective comprehension. To address these challenges, we propose the Cognitive-Level Alignment Framework (CLAF), a general-purpose generation framework that aligns both knowledge complexity and presentation style with user cognition. CLAF integrates a capability-aware retrieval module based on a hierarchical knowledge graph and a style optimization module guided by Bloom's taxonomy and preference learning. Additionally, a knowledge-controllable generation component ensures consistency and relevance throughout the output. To support training and evaluation, we construct SCALE, a cognitively annotated dataset containing responses at multiple comprehension levels per query. Empirical results show that CLAF enhances the adaptability and informativeness of LLM outputs across a range of user profiles, offering a robust solution to cognitive-level alignment in real-world applications.