We propose UPSA, a novel approach that accomplishes Unsupervised Paraphrasing by Simulated Annealing. We model paraphrase generation as an optimization problem and propose a sophisticated objective function, involving semantic similarity, expression diversity, and language fluency of paraphrases. UPSA searches the sentence space towards this objective by performing a sequence of local editing. We evaluate our approach on various datasets, namely, Quora, Wikianswers, MSCOCO, and Twitter. Extensive results show that UPSA achieves the state-of-the-art performance compared with previous unsupervised methods in terms of both automatic and human evaluations. Further, our approach outperforms most existing domain-adapted supervised models, showing the generalizability of UPSA.