Remanufacturing that returns used products to a like-new condition, is essential for promoting the circular economy and reducing carbon emissions. The optimal design of remanufacturing process (ODRP), as a knowledge-intensive complex decision-making task, plays a vital role in the success of remanufacturing. However, insufficient utilization of remanufacturing knowledge, and the trade-offs among multi-objectives in decision-making scenarios make ODRP time-consuming and labor-intensive. With the development of next-generation artificial intelligence (AI) technologies, large language models (LLMs) provide an important enabling tool for complex decision-making tasks. However, existing LLMs still face significant challenges in ODRP due to a lack of remanufacturing knowledge and computational capabilities. To address this issue, an LLM-based approach augmented with knowledge and function is proposed in this paper. Firstly, based on the establishment of remanufacturing process database, a retrieval augmented generation (RAG)-based knowledge-augmented strategy is designed to retrieve failure information (e.g., failure form, failure degree, etc.) of returned products through the interaction with LLMs, and generate the feasible remanufacturing schemes. Secondly, a function-augmented mechanism with function learning is also proposed to calculate each objective value and combined assessed value of the generated remanufacturing schemes with LLMs, assisting process designers in designing optimal remanufacturing scheme and process parameters. Finally, the proposed approach is validated using a case study on automobile gearbox remanufacturing. The results indicate that the proposed knowledge-augmented strategy improves the average accuracy from 65% to 79% when using ChatGLM3-6B as the base LLMs. Additionally, the proposed function-augmented mechanism can calculate the minimum combined assessed value and make more realistic results for ODRP. Meanwhile, the proposed integrated approach provides a solution to knowledge-intensive and complex decision-making tasks, which has a broad application prospect.