Cross-Domain Sequential Recommendation (CDSR) aims to mine and transfer users' sequential preferences across different domains to alleviate the long-standing cold-start issue. Traditional CDSR models capture collaborative information through user and item modeling while overlooking valuable semantic information. Recently, Large Language Model (LLM) has demonstrated powerful semantic reasoning capabilities, motivating us to introduce them to better capture semantic information. However, introducing LLMs to CDSR is non-trivial due to two crucial issues: seamless information integration and domain-specific generation. To this end, we propose a novel framework named URLLM, which aims to improve the CDSR performance by exploring the User Retrieval approach and domain grounding on LLM simultaneously. Specifically, we first present a novel dual-graph sequential model to capture the diverse information, along with an alignment and contrastive learning method to facilitate domain knowledge transfer. Subsequently, a user retrieve-generation model is adopted to seamlessly integrate the structural information into LLM, fully harnessing its emergent inferencing ability. Furthermore, we propose a domain-specific strategy and a refinement module to prevent out-of-domain generation. Extensive experiments on Amazon demonstrated the information integration and domain-specific generation ability of URLLM in comparison to state-of-the-art baselines. Our code is available at https://github.com/TingJShen/URLLM