He graduated from the Leningrad Higher Combined Arms Command School named after S. M. Kirov in 1966.

[2] Grekov graduated from the Military Academy of the General Staff of the Armed Forces of the USSR named after K. E. Voroshilov in 1985.

[2] From 1985, he was Chief of Staff and First Deputy Army Commander in the Leningrad Military District.

[2] In 1986, he was the Chief of Staff - First Deputy Commander of the 40th Army as part of a limited contingent of Soviet troops in Afghanistan.

[2] In 1989, he was the first deputy commander of the Transcaucasian Military District,[4][2] and had participated in the localization of the Armenian-Azerbaijani armed conflict in Nagorno-Karabakh.