Teispes (flourished 7th century bc) was an early Achaemenid Persian king (reigned c. 675–c. 640), the forefather of the great kings Darius I and Cyrus II.
He was, perhaps, the son of Achaemenes, whose name was given to the Achaemenid dynasty. Teispes ruled the district of Anshan in Elam (north of the Persian Gulf) and tried to maintain a neutral position between the powerful kingdoms of Elam and Assyria. At his death, Teispes either divided his kingdom between his sons, Ariaramnes and Cyrus I, or provided for an alternation in succession between the senior and junior lines.