The advent of Artificial Intelligence Generated Content (AIGC), particularly large language models (LLMs), presents a transformative opportunity for addressing long-standing challenges in Business English Writing instruction. Traditional teaching models often struggle with providing timely, personalized feedback and creating authentic, scalable practice scenarios due to high teacher workload and heterogeneous student proficiency levels. This paper proposes a novel Precision Teaching model empowered by AIGC, designed to overcome these limitations. The model conceptualizes a dynamic teaching process comprising three core stages: AIGC-powered precise diagnostic analysis, AIGC-facilitated personalized learning cycles, and AIGC-assisted multidimensional holistic evaluation. It fundamentally redefines the roles of teachers and students, advocating for a "human-AI synergy" where AIGC handles repetitive tasks like initial drafting, grammar checking, and scenario generation, freeing teachers to focus on higher-order instruction such as critical thinking, strategic communication, and ethical application. A preliminary practice study conducted within an undergraduate Business English program demonstrated the model's efficacy in enhancing students' writing accuracy, genre awareness, and learning motivation. The study also revealed challenges, including prompt engineering proficiency and the need for AI literacy training. The paper concludes that the AIGC-empowered Precision Teaching model offers a viable and innovative pathway for achieving student-centered, data-informed, and practically oriented reform in Business English Writing education, while also highlighting imperative considerations for academic integrity and pedagogical adaptation.