Fyodor Ivanovich Beggrov (also spelled Begrov; 1835–1885) was a Russian pianist and music teacher. He was born in St. Petersburg, Russian Empire, into the family of the engraver Ivan Petrovich Beggrov. His uncle Karl was a lithographer and watercolor painter, and his brother Ivan was an engineer-technologist who founded Russia's first printing-ink factory.
Beggrov studied at the Annenschule, where he quickly showed musical ability and was already appearing successfully in concerts by the age of ten. He continued his piano training with Anton Gerke.
In 1855, Beggrov entered the Leipzig Conservatory. His teachers there included Ignaz Moscheles, Moritz Hauptmann, Ernst Friedrich Eduard Richter, and Rietz.
After returning to St. Petersburg, Beggrov joined the St. Petersburg Conservatory as a piano teacher at the invitation of Anton Rubinstein. He taught there until 1879 and, from 1870, also served as music inspector at the Mariinsky Institute. In 1872, he became one of the founders of the St. Petersburg Chamber Music Society.
He retired because of ill health and settled abroad. Among his pupils, the pianist Polina Bertenson (Voronets) became particularly well known after graduating brilliantly from the St. Petersburg Conservatory and giving many successful concerts.
Beggrov died in Stuttgart, German Empire, in 1885.