Open-Domain Question Answering (ODQA) requires models to answer factoid questions with no context given. The common way for this task is to train models on a large-scale annotated dataset to retrieve related documents and generate answers based on these documents. In this paper, we show that the ODQA architecture can be dramatically simpliﬁed by treating Large Language Models (LLMs) as a knowledge corpus and pro-pose a Self-Prompting framework for LLMs to perform ODQA so as to eliminate the need for training data and external knowledge corpus. Concretely, we ﬁrstly generate multiple pseudo QA pairs with background passages and one-sentence explanations for these QAs by prompting LLMs step by step and then leverage the generated QA pairs for in-context learning. Experimental results show our method surpasses previous state-of-the-art methods by +8.8 EM averagely on three widely-used ODQA datasets, and even achieves comparable performance with several retrieval-augmented ﬁne-tuned models.