Kapustin studied piano with Avrelian Rubakh (pupil of Felix Blumenfeld who also taught Simon Barere and Vladimir Horowitz) and, later, Alexander Goldenweiser at the Moscow Conservatory. During the 1950s he acquired a reputation as a jazz pianist, arranger and composer. He is steeped, therefore, in both the traditions of classical virtuoso pianism and improvisational jazz.
He fuses these influences in his compositions, using jazz idioms in formal classical structures. A striking example of this is his Suite in the Old Style op. 28, written in 1977, which inhabits the sound world of jazz improvisation but is modelled on baroque suites such as the keyboard partitas composed by J. S. Bach, each movement being a stylised dance or a pair of dances in strict binary form. Other examples of this fusion are his set of 24 Preludes and Fugues op. 82 written in 1997, and the op. 100 Sonatina.
Kapustin views himself as a composer rather than a jazz musician. He has said, "I was never a jazz musician. I never tried to be a real jazz pianist, but I had to do it because of the composing. I'm not interested in improvisation and what is a jazz musician without improvisation? All my improvisation is written, of course, and they became much better; it improved them."
Among his works are 18 piano sonatas, six piano concerti, other instrumental concerti, sets of piano variations, Etudes and concert studies; see list of compositions by Nikolai Kapustin.
Russian and Japanese record labels have released several recordings of the composer playing his own music. He has also been championed by a number of prominent western pianists, including Steven Osborne and Marc-André Hamelin who both released CDs devoted to Kapustin.