Grechkin was born on 26 March 1893 in the village of Karpenka, Novouzensky Uyezd in Samara Governorate (now Krasnokutsky District, Saratov Oblast).

In 1914, after the beginning of World War I, Grechkin was drafted into the Imperial Russian Army, serving in the reserve battalion of the Lifeguard Izmaylovsky Regiment.

[2] Grechkin joined the Red Army in August 1918 and was appointed assistant commissar of the staff of the Don Soviet Republic.

He fought in battles with the White Army 4th Don Cavalry Corps, the elimination of Sergei Ulagay's landing force, and the suppression of partisans in the Kuban.

Between April and July 1931, he led the regiment in battles with Ibrahim Bek, the leader of the Muslim Basmachi insurgent movement.

In 1939, he graduated from the Courses of Improvement for Higher Officers (KUVNAS) at the Military Academy of the General Staff, and in September fought in the Soviet invasion of Poland.

[2][3] During the first months after Operation Barbarossa, the 22 June 1941 German invasion of the Soviet Union, Grechkin was tasked with organizing the construction of the Mius defensive line, which protected Rostov-on-Don.

Grechkin became commander of the 56th Army operational group in October, leading it in the defense of Rostov, which ended in a retreat from the city.

During February 1943, he led the 18th Army operational group tasked with organizing and training amphibious assault troops south of Novorossiysk.

In February 1951, he became head of the special department for accelerated training at the Military Institute of Foreign Languages, and retired in June 1954.