Laub was born in Prague from a German Bohemian family which had assimilated into the ethnic Czech community.
His first solo concert was at age ten in the Stavovské divadlo (a theater in Prague).
From 1866 to 1874 he was professor of violin at the Moscow Conservatory, where his many notable students included Stanisław Barcewicz.
He was the first violinist in the premiere performances of both Tchaikovsky's First and Second String Quartets, and the posthumous dedicatee of the Third of 1876.
He died on the way to a spa in Meran, in Gries-San Quirino [it] near Bolzano, and is interred in the Vyšehrad cemetery.