Conversational retrieval leverages multi-turn conversations to meet users’ information needs, and accurately understanding the new intent has become a significant challenge in this field. Recently, the language comprehension and reasoning capabilities of large language models (LLMs) offer a viable solution to these challenges. In this article, we propose a new Dual-Query Generation and Joint-Encoding method by utilizing LLM for Conversational Information Seeking, abbreviated as DQ-CIS. Specifically, we propose a dual-query generation approach that leverages both open source and closed source LLMs to generate two complementary queries: a full-rewrite query that preserves the context semantics of the conversation and a condensed-rewrite query that emphasizes the core intent of the current query. Additionally, to better express the semantic information of the query, we propose a dual-query joint-encoding method, which enhances the thematic expression of query vectors by treating the dual-query as semantic complementary. A query coverage fine-tuned semantic matching method is also introduced to improve result relevance and ranking by fine-tuning the original retrieval scores by ColBERT. We conducted a number of experiments on seven publicly available conversational retrieval datasets. The results show that compared with other models, DQ-CIS has strong competitiveness in both retrieval efficiency and retrieval results.