Dense retrieval is an effective information retrieval technique that utilizes semantic embedding similarity to retrieve documents. There are two typical kinds of dense retrieval methods, i.e., training-based methods and zero-shot methods. Training-based dense retrieval can achieve relatively high retrieval accuracy, but it relies on annotated datasets to train similarity retrieval models with high resource consumption. On the contrary, zero-shot dense retrieval does not require training-specific models, but its retrieval accuracy needs to be improved. To improve the accuracy of zero-shot dense retrieval, we propose a novel zero-shot dense retrieval based on query expansion (ZRQE). Specifically, it divides dense retrieval into two tasks: generating relevant documents using an instruction-following language model and dense retrieval by calculating vector similarity. The experimental results show that ZRQE achieves higher retrieval accuracy than other state-of-the-art dense retrieval methods.