Verifiable generation aims to let the large language model (LLM) generate text with corresponding supporting documents, which enables the user to flexibly verify the answer and makes it more trustworthy. Its evaluation not only measures the correctness of the answer, but also the answer's verifiability, i.e., how well the answer is supported by the corresponding documents. In typical, verifiable generation adopts the retrieval-read pipeline, which is divided into two stages: 1) retrieve relevant documents of the question. 2) according to the documents, generate the corresponding answer. Since the retrieved documents can supplement knowledge for the LLM to generate the answer and serve as evidence, the retrieval stage is essential for the correctness and verifiability of the answer. However, the widely used retrievers become the bottleneck of the entire pipeline and limit the overall performance. They often have fewer parameters than the large language model and have not been proven to scale well to the size of LLMs. Since the LLM passively receives the retrieval result, if the retriever does not correctly find the supporting documents, the LLM can not generate the correct and verifiable answer, which overshadows the LLM's remarkable abilities. In this paper, we propose LLatrieval (Large Language Model Verified Retrieval), where the LLM updates the retrieval result until it verifies that the retrieved documents can support answering the question. Thus, the LLM can iteratively provide feedback to retrieval and facilitate the retrieval result to sufficiently support verifiable generation. Experimental results show that our method significantly outperforms extensive baselines and achieves new state-of-the-art results.