The invention provides a process for preparing bromine-containing polymers, comprising a Friedel-Crafts alkylation reaction of pentabromobenzyl halide with a polymer reactant which contains one or more six-membered aromatic ring(s) in its repeat unit, in the presence of at least one Friedel-Crafts catalyst. The so-formed bromine-containing polymers, having pendent —CH2C6Br5 groups attached to at least a portion of the six-membered aromatic rings of the polymer, with a carbon ring atom of said six-membered aromatic ring being bonded to the aliphatic carbon of said —CH2C6Br5 pendent group, are also provided. These bromine-containing polymers are useful as flame retarding agents.