His father, Nicolae Grigore, was a fighter pilot in the Romanian Air Force and a World War II hero (subsequently promoted to general); one street in Bucharest is named after him.

Eugenia Ionescu used to hold musical soirees in her home, where she would invite famous pianists and teachers of the time to listen to him, including Florica Musicescu, Cella Delavrancea, Constanța Erbiceanu, Muza Ciomac, Silvia Șerbescu, Nadia Chebap, and Madeleine Cocorăscu, among others.

It was during these musical soirees that Dan Grigore was discovered by the famous composer and professor Mihail Jora (member of the Romanian Academy), a close friend of George Enescu and former teacher of Dinu Lipatti.

Given the family's hardship and the child's unusual talent, Mihail Jora (although in financial trouble himself due to similar political reasons) generously offered to give Grigore private lessons free of charge, which he did for the next seven years (between 1955-1962).

In 1957, the fourteen-year-old Grigore made his first appearance on stage with three recently discovered works of George Enescu in first world audition (Chorale, Burlesque, and Carillon nocturne from the Piano Suite no.

[2] In 1968, the famous professor and conductor Nadia Boulanger offered Grigore a full scholarship at the American Conservatory in Fontainebleau, which was denied by the Romanian Communist regime.