Rafael Grigorian trained at the Baku Choreographic Institute and at the Kirov Ballet School in Leningrad under the instruction of A.I. Pushkin. For 20 years, he was a principal dancer with the Baku Theater of Opera and Ballet. In 1980 Grigorian was awarded Laureate of the State of the USSR, and he received the prestigious title of the People's Artist of Azerbaijan, SSR in 1982.
Grigorian has toured extensively in Europe and Asia with the stars of the Kirov and Bolshoi Ballet theaters. He served as instructor of the Moscow Ballet Festival under the leadership of Bolshoi Ballet Soloist S. Radchenko. From 1986 until 1991, he held the title of choreographer for the Moscow School of Ice Dancing. Several of his students are Olympic and World competition gold and silver ice dancing medalists.
In 1991, Grigorian opened Rafael Grigorian's School of Classical Ballet in Corning and Elmira, New York, and has since opened a branch of his school in Binghamton, New York. He is also the founder and artistic director of the Rafael Grigorian Ballet Theatre. In 1996 Grigorian received the prestigious Arts Partnership Award for the Arts of the Southern Finger Lakes for his outstanding contribution to the arts of the Southern Tier communities.