Graphic design, which has been evolving since the 15th century, plays a crucial role in advertising. The creation of high-quality designs demands creativity, innovation, and lateral thinking. This intricate task involves understanding the objective, crafting visual elements such as the background, decoration, font, color, and shape, formulating diverse professional layouts, and adhering to fundamental visual design principles. In this paper, we introduce COLE, a hierarchical generation framework designed to comprehensively address these challenges. This COLE system can transform a straightforward intention prompt into a high-quality graphic design, while also supporting flexible editing based on user input. Examples of such input might include directives like ``design a poster for Hisaishi's concert.'' The key insight is to dissect the complex task of text-to-design generation into a hierarchy of simpler sub-tasks, each addressed by specialized models working collaboratively. The results from these models are then consolidated to produce a cohesive final output. Our hierarchical task decomposition can streamline the complex process and significantly enhance generation reliability. Our COLE system consists of multiple fine-tuned Large Language Models (LLMs), Large Multimodal Models (LMMs), and Diffusion Models (DMs), each specifically tailored for a design-aware text or image generation task. Furthermore, we construct the DESIGNERINTENTION benchmark to highlight the superiority of our COLE over existing methods in generating high-quality graphic designs from user intent. We perceive our COLE as an important step towards addressing more complex visual design generation tasks in the future.