Maximov was born to a peasant family in the village of Lopino in the Saint Petersburg Governorate, near Novaya Ladoga.

Maximov painted the Sick Child (1864) at that time, when received a Gold Medal of the Academia.

In 1865 he (like the group of fourteen led by Ivan Kramskoi had done earlier) refused to take part in the competitions for the Major Gold Medal by Academia.

Indeed, after graduation from the Academia he moved to the village of Shubino, in the gubernia of Tver, where he painted the peasant life, earning money as a painting teacher of the Princes Golenischev-Kutuzov (descendants of Mikhail Illarionovich Kutuzov).

His painting Grandmother's tales (1867) was shown at an exhibition of the Imperial Society for the Encouragement of the Arts, where it won a prize and was bought by Pavel Tretyakov.