Alexander Grinberg was born in Charkov, Ukraine. In 1980 he graduated from the Charkov Music College and five years later he successfully completed I. Kovach’s Composition class at the Charkov Academy of Art. In 1992 Alexander Grinberg participated in the composition master class with Poul Ruders and Edisson Denissow in Lerchenborg, Denmark.
From 1987–1995 Alexander Grinberg taught Composition, Ear Training, and Music Literature at a music school in Charkov. In 1987–1994 and 2000–2003 he taught Composition, Polyphony, and Music Literature at the Charkov Music College.
From 1994–2003 Grinberg read Composition, Instrumentations Science, Polyphony, as well as Composition Technique of the 20th century music at the Charkov Academy of Art.
In 1999 he was rewarded the Slatin Prize of the City Charkov.
In March 2001 he acted as a juror at the Ukraine Composition Competition “Gradus ad Parnassum.”
In 2003 Alexander Grinberg moved to Düsseldorf.
From 2005–2006 he taught Musicology at the Folkwang University in Essen, and since April 2008 he has been teaching Music Theory, Piano, and Composition in Düsseldorf.