Flavius Anicius Hermogenianus Olybrius (fl. 395-397) was a politician and aristocrat of the Roman Empire.
Olybrius was the son of Sextus Petronius Probus, one of the most influential men of his era and consul in 371, and of Anicia Faltonia Proba; his brothers were Anicius Probinus, Anicius Petronius Probus and sister Anicia Proba.
Olybrius was raised with his brother Probinus in Rome, where he was born. He divided with his brother the consulate in the year 395, while both were very young; on this occasion to the two brothers was dedicated a panegyric by Claudian (Panegyricus de consulatu Probini et Olybrii). Although they originated in a family belonging to the Roman senatorial aristocracy, traditionally pagan, Olybrius and Probinus were Christians; the appointment as consuls of these two Christians may have been a signal, desired by the emperor Theodosius I, the very next year to the usurpation and Pagan restoration of Eugenius.
With his brother he received the dedication of the work Exempla elocutionum by Arusianus Messius, and both received a letter (Epistles, v) by Quintus Aurelius Symmachus in 397.
He married his relative Anicia Iuliana and had one son and one daughter, Demetrias.