Born in Wenden (now Cesis, Latvia) 3 (15) July 1889 in the family working. Studied in Riga, first in Manusrisco nautical school (1904−1907), and then in the municipal drawing school (V. Purvitis), from which he graduated in 1914. He was a circle of young Latvian modernists «Green flower». Having settled in Moscow in 1914 and married the painter N. Udaltsova, was friends with the soldiers-revolutionaries from Latvia. In 1920−1932 was a member of the Institute of artistic culture (INKhUK) and a teacher at the Higher artistic-technical workshops (VHUTEMAS).During the Stalinist «great terror» Drevin was arrested and executed on 26 February 1938
The son of a worker. Fifteen years arrived in Riga nautical school. In 1908−1913 he studied at the Riga City drawing school under V. Purvitis. By the mid-1910s, became interested in the modernist trends in painting and in 1914 became one of the founders of the Association of young Latvian avant-garde artists «Green flower» (Lett. Zaļā pukë), but he was immediately forced his family to move to Moscow, where he joined the group «Jack of diamonds». After the October revolution, in the course of the year led the art Studio of the Latvian Riflemen in Latvian National the Commissariat, where, in particular, met with his friend on the «Green flower» by Karl Johansson.
In the first years after Drevin was spotted by Malevich and Tatlin Drevin was offered a job in the Department of fine arts of people’s Commissariat of education. In 1920 Drevin taught at the VKhUTEMAS, was the leader of the workshop till the close of the Institute in 1930, then Drevin moved away from teaching and was engaged only in painting, entering in 1931, part of the artistic group «Thirteen».
Since the mid-1920s Drevin and his wife, artist Nadezhda Udaltsova travel a lot around the Soviet Union, actively working on the landscapes of the Urals, Altai, Eastern Kazakhstan, and Armenia.
January 17, 1938 Alexander Drevin was arrested under fabricated cases of conspiracy Latvian Riflemen and after a short poznawania shot at Butovo. When arrested, his wife saved the paintings Drevin from seizure, giving them their own. They were first exhibited in Moscow in 1971.