E-commerce authoring involves creating attractive, abundant, and targeted promotional content to drive product sales. The emergence of large language models (LLMs) introduces an innovative paradigm, offering a unified solution to address various authoring tasks within this scenario. However, mainstream LLMs trained on general corpora with common sense knowledge reveal limitations in fitting complex and personalized features unique to e-commerce products and customers. Furthermore, LLMs like GPT-3.5 necessitate remote accessibility, raising concerns about safeguarding voluminous customer privacy data during transmission. This paper proposes the LLaMA-E, the unified and customized instruction-following language models focusing on diverse e-commerce authoring tasks. Specifically, the domain experts create the seed instruction set from the tasks of ads generation, query-enhanced product title rewriting, product classification, purchase intent speculation, and general Q&A. These tasks enable the models to comprehensively understand precise e-commerce authoring knowledge by interleaving features covering typical service aspects of customers, sellers, and platforms. The GPT-3.5 is introduced as a teacher model, which expands the seed instructions to form a training set for the LLaMA-E models with various scales. The experimental results show that the proposed LLaMA-E models achieve state-of-the-art results in quantitative and qualitative evaluations, also exhibiting the advantage in zero-shot scenes. To the best of our knowledge, this study is the first to serve the LLMs to specific e-commerce authoring scenarios.