Contrastive learning has been the dominant approach to train state-of-the-art sentence embeddings. Previous studies have typically learned sentence embeddings either through the use of human-annotated natural language inference (NLI) data or via large-scale unlabeled sentences in an unsupervised manner. However, even in the case of unlabeled data, their acquisition presents challenges in certain domains due to various reasons. due to copyright restrictions, data distribution issues, and messy formats, among other factors. To address these issues, we present SynCSE, a contrastive learning framework that trains sentence embeddings with synthetic data. Specifically, we explore utilizing large language models to synthesize the required data samples for contrastive learning, including (1) producing positive and negative annotations given unlabeled sentences SynCSE-partial, and (2) generating sentences along with their corresponding annotations from scratch SynCSE-scratch. Notably, SynCSE-scratch constitutes the first contrastive learning method to learn sentence embeddings from scratch without manually collecting any data sample. Experimental results on sentence similarity and reranking tasks indicate that both SynCSE-partial and SynCSE-scratch greatly outperform unsupervised baselines, and SynCSE-partial even achieves comparable performance to the supervised models in most settings.