Year 337 (CCCXXXVII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Felicianus and Titianus (or, less frequently, year 1090 Ab urbe condita). The denomination 337 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

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• Faxian, Chinese Buddhist monk, traveler (approximate date)
• Fú Jiān, emperor of the Chinese Di state Former Qin (d. 385)
• Lü Guang, founding emperor of the Di state Later Liang (d. 400)
• Zenobius of Florence, Italian bishop and wonderworker (d. 417)

• January 13 – Leontius of Caesarea, Roman Catholic bishop and saint
• February 21 – Eustathius the Great, patriarch of Antioch (approximate date)
• May 22 – Constantine the Great, emperor of the Roman Empire, Orthodox priest and saint^[2]
• May 27 – Flavius Dalmatius, father of Dalmatius and Hannibalianus (executed)
• August 30 – Alexander of Constantinople, bishop of Byzantium (approximate date)
• September 11 – Julius Constantius, son of Constantius Chlorus (executed)
• September 24 – Hannibalianus, king of the Pontus and nephew of Constantine I (executed)
• September 27 – Dalmatius, Caesar and nephew of Constantine I (executed)