After serving in World War I as an Imperial Russian Army officer, Grechkin joined the Red Army in 1918 and fought in the Russian Civil War. He rose through the ranks in the interwar period and commanded a division in the Winter War. After the Operation Barbarossa, the German invasion of the Soviet Union, Grechkin temporarily commanded the North Caucasus Military District, and as commander of the 56th Army operational group, led troops in the Battle of Rostov. He commanded the 9th Army and the 28th Army in 1943 and was deputy commander of the 3rd Baltic Front in the summer of 1943. After the war, Grechkin successively commanded two rifle corps and the Vystrel commander improvement courses before his 1954 retirement.