Pospelov (Russian: Поспе́лов), female form Pospelova (Russian: Поспе́лова), is a Russian surname. Notable people with this surname include:
- Aleksandra Pospelova (born 1998), Russian tennis player
- Dmytro Pospelov (born 1991), Ukrainian football player
- Maria V. Pospelova-Shtrom (1902–1991), Russian entomologist
- Pyotr Pospelov (1898–1979), Soviet scientist and functionary
- Svetlana Pospelova (born 1979), Russian sprinter