We introduce CVSS, a massively multilingual-to-English speech-to-speech translation (S2ST) corpus, covering sentence-level parallel S2ST pairs from 21 languages into English. CVSS is derived from the Common Voice speech corpus and the CoVoST 2 speech-to-text translation (ST) corpus, by synthesizing the translation text from CoVoST 2 into speech using state-of-the-art TTS systems. Two versions of translation speeches are provided: 1) CVSS-C: All the translation speeches are in a single high-quality canonical voice; 2) CVSS-T: The translation speeches are in voices transferred from the corresponding source speeches. In addition, CVSS provides normalized translation text which matches the pronunciation in the translation speech. On each version of CVSS, we built baseline multilingual direct S2ST models and cascade S2ST models, verifying the effectiveness of the corpus. To build strong cascade S2ST baselines, we trained an ST model on CoVoST 2, which outperforms the previous state-of-the-art trained on the corpus without extra data by 5.8 BLEU. Nevertheless, the performance of the direct S2ST models approaches the strong cascade baselines when trained from scratch, and with only 0.1 or 0.7 BLEU difference on ASR transcribed translation when initialized from matching ST models.