Neverkinsky District (Russian: Неве́ркинский райо́н; Tatar: Невер районы, romanized: Never rayonı) is an administrative[1] and municipal[4] district (raion), one of the twenty-seven in Penza Oblast, Russia.

It is located in the southeast of the oblast.

The area of the district is 984.5 square kilometers (380.1 sq mi).

[2] Its administrative center is the rural locality (a selo) of Neverkino.

[3] The highest point of Penza Oblast is an unnamed hill of the Khvalynsk Mountains reaching 342 metres (1,122 ft) above sea level located in the district.