Text-to-SQL aims at generating SQL queries for the given natural language questions and thus helping users to query databases. Prompt learning with large language models (LLMs) has emerged as a recent approach, which designs prompts to lead LLMs to understand the input question and generate the corresponding SQL. However, it faces challenges with strict SQL syntax requirements. Existing work prompts the LLMs with a list of demonstration examples (i.e. question-SQL pairs) to generate SQL, but the fixed prompts can hardly handle the scenario where the semantic gap between the retrieved demonstration and the input question is large. In this paper, we propose a retrieval-augmented prompting method for a LLM-based Text-to-SQL framework, involving sample-aware prompting and a dynamic revision chain. Our approach incorporates sample-aware demonstrations, which include the composition of SQL operators and fine-grained information related to the given question. To retrieve questions sharing similar intents with input questions, we propose two strategies for assisting retrieval. Firstly, we leverage LLMs to simplify the original questions, unifying the syntax and thereby clarifying the users' intentions. To generate executable and accurate SQLs without human intervention, we design a dynamic revision chain which iteratively adapts fine-grained feedback from the previously generated SQL. Experimental results on three Text-to-SQL benchmarks demonstrate the superiority of our method over strong baseline models.