Addai is a Syriac given name, equivalent to Thaddeus. It may refer to:
- Addai I, also known as Thaddeus of Edessa (1st/2nd century AD), saint and evangelist of Edessa
- Addai II Giwargis, patriarch of the Ancient Church of the East since 1970
- Addai Scher (1867–1915), the Chaldean Catholic archbishop of Siirt