Alexei was born to the family of a government official who worked in the Armory and in the "Канцелярия от строений" (Chancellory of Buildings).
Here he met prince Ivan Shuvalov who supported Antropov's work for the rest of his life.
From 1757 to 1759 Antropov returned to Saint-Petersburg and obtained further instruction from court painter Pietro Rotari of Italy.
At that time, artists preferred a soft combinations of colors and some flattering for the ceremonial portraits.
Antropov preferred the traditional icon and parsuna portraits, based on a sharp contrast of colors with a dark background.
In 1789 Antropov made a personal sacrifice, transferring his only house to the Department of Education for organizing a Free School there.
In 1795 Antropov died of a fever and was buried in the Lazarevskoe Cemetery at the Alexander Nevsky Monastery, in Saint Petersburg.