Feith was born of into an aristocratic family in Zwolle, the capital of the province Overijssel as the only son of Pieter Feith and Elsabe Spaar. He was christened on 09 Feb 1753. He was educated at Harderwijk and studied law at the university of Leiden (1769-1770), where he took his degree after only one year. He married Ockje Groeneveld in Weener, Germany, in Nov 1772 and settled in his birthplace. In the period Sep 1773 through to Jan 1790 they had at least 10 children, all christened in Zwolle. In 1780 Rhijnvis Feith became burgomaster of Zwolle.
He built a luxurious villa, which he named Boschwijk, in Zalné in Zwollerkerspel, the outskirts of Zwolle, and there he lived in the greatest comfort. His first important production was Julia, in 1783, a novel written in emulation of Werther, and steeped in Weltschmerz and despair. This was followed by the tragedy of Thirsci (1784); Ferdinand and Constantia (1785), another Werther novel; and The Patriots (1784), a tragedy. Bilderdijk and other writers attacked his morbid melancholy, and Johannes Kinker (1764–1845) parodied his novels, but his vogue continued. In 1791 he published a tragedy of Lady Jane Grey; in 1792 a didactic poem, The Grave (Dutch: Het Graf), in four cantos; in 1793 Inez de Castro; in 1796 to 1814 five volumes of Odes and Miscellaneous Poems; and in 1802 Old Age (Dutch: De Ouderdom), in six cantos. He wrote Letters to Sophia on Kant's Philosophy, a poetical work, in 1805. In 1808 he became member of the Royal Institute. His Letters on Different Subjects of Literature of 1784 was a noted piece of literary criticism. He died in Zwolle in 1824.
His works were collected (Rotterdam, 11 vols.) in 1824, with a biographical notice by N. G. van Kampen. Though now neglected, he is interesting as the Dutch representative of the mood that in Germany produced Novalis.