Born at Alexandria, perhaps about 270 BCE, Apollonius was a pupil of Callimachus. Callimachus' "Hymn to Apollo", closes with some lines that allude to Apollonius, and dates about 248 or 247 BCE, which would put Apollonius' birth about twenty years earlier. In his Argonautica the young poet departed from Callimachus's learned and artificial style and aimed instead to recreate a Homeric simplicity. He recited an early version while stil scarcely more than a youth, but the poem got a poor reception in Callimachus' learned circle at the Library. The quarrel between the older and younger poet degenerated into a bitter personal feud, commemorated in surviving epigrams. Apollonius retired in disgust to Rhodes. There his labors as a teacher of rhetoric and his newly revised poem won him hearty recognition and even admission to citizenship, whence his surname. Afterwards, returning to Alexandria, he recited his poem once more, this time with universal applause, and he was reconciled with Callimachus, next to whom he was eventually buried. Apollonius succeeded Eratosthenes as head of the Alexandrian Library.
The scanty biographical information on Apollonius comes from two brief "lives" in the Scholia.
The adventure of the Argonauts had been told often before in verse and prose. Only notes of the authors' names survive; their works have perished. The one well-known earlier surviving account is in Pindar's fourth Pythian ode, which provided Apollonius with some details. Epic unity escaped Apollonius, and his epic in four books resolves into a string of well-told episodes, the most memorable being the love story of Jason and Medea in Book iii.