Most of the state-of-the-art methods for abstractive text summarization are under supervised learning settings, while heavily relying on high-quality and large-scale parallel corpora. In this paper, we remove the need for reference summaries and present an unsupervised learning method SCR (Summarize, Contrast and Review) for abstractive summarization, which leverages contrastive learning and is the first work to apply contrastive learning for unsupervised abstractive summarization. Particularly, we use the true source documents as positive source document examples, and strategically generated fake source documents as negative source document examples to train the model to generate good summaries. Furthermore, we consider and improve the writing quality of the generated summaries by guiding them to be similar to human-written texts. The promising results on extensive experiments show that SCR outperforms other unsupervised abstractive summarization baselines, which demonstrates its effectiveness.