Story of the bow of Parashuram in the Ramayana is found in the Bala Kanda of the Ramayana. Parashuram himself narrates about its glory to Sri Ram. An angry Parashuram stops the marriage party of Sri Ram in the deep dense forest. Parashuram had heard that that Sri Ram had married Mata Sita after breaking the bow of Mahadev Shiva.
The bow of Parashuram like that of the Mahadeva was made by Vishwakarma. It was used by Narayana.
Rishi Richaka had received the bow from Narayana. The Rishi had given the bow to his son Jamadagni, father of Parashurama. This bow was used to kill innumerable kings on earth who were spreading Adharma.
Parashuram then challenges Sri Ram to lift the bow and tie the string and shoot an arrow. This task is easily performed by Sri Ram.
Parashuram abandons the bow after He realizes that his worthy successor to defend Dharma had appeared on earth in the form of Sri Rama.
Rama then gave the bow to Varuna, the god of the oceans.