Mozes Crost was a son of  Ephraim Crost and Bloeme Trompetter. He married Anna Speelman in Amsterdam on 4 August 1921, a daughter of Israel Speelman and Anna Catherina Sombogaart. The couple had two children, of whom one daughter has survived the Holocaust.

Mozes Crost was born into a family of seven children, of whom three children have survived the Holocaust. The other four, he self, Esther, Rachel and Levie have been killed during the Shoah.

City Archive of Amsterdam, archive card of  Mozes Crost, family registration card of Ephraim Crost and website www.wiewaswie.nl.