The child star, now 37, is back in Russia and will play Sunday at the Conservatory.
Kissin was recognized as a child prodigy at the Gnesin School of Music for talented children where he gave his first solo concerts for the pupils.
"My parents never pushed me on stage, nor did my piano teacher, Anna Pavlovna Kantor. They were trying to limit my public appearances as much as they possibly could," said Kissin in an interview with BBC Music magazine.
Nevertheless, Kissin gave his first major concert in the Great Hall of the Moscow Conservatory at the age of 15 and was soon selling out concerts in Europe.
Five years later, he debuted in the United States during Carnegie Hall's centennial season, and soon afterward his family emigrated to the United States, where his fame has continued to grow.
He has played at the Grammys Award ceremony, and in 2006 he himself won a Grammy, after being nominated 10 times, for a recording of Russian piano music.
Whenever Kissin tours the United States, Europe and Japan, he is swamped in flowers after concerts. One concert in Korea saw 110 people come with bouquets.
His visits to Russia are rare; he last played a year ago at a concert for the poet Andrei Vosnesensky, and each of his concerts is a huge cultural event.
Kissin will play at the Conservatory's Great Hall with the Virtuosos of Moscow Chamber Orchestra in honor of the orchestra's 30th anniversary. As always, Vladimir Spivakov will conduct.
Together, they will perform Beethoven's Concerto For Piano And Orchestra No.1 as well as compositions by Schoenberg and Bach.
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