Fluorinated block copolymers poly(2,3,4,5,6-pentafluorostyrene)-b-poly(styrene) (PFS-b-PS) synthesized by atom transfer radical polymerization was functionalized with quaternary ammonium base groups via chloromethylation of PFS-b-PS, followed by reactions with trimethylamine and ion exchange with KOH to prepare anion exchange block polymer electrolytes (AEBPEs). The challenges and limitations during the synthesis are discussed. A comparative study on the chloromethylation of PFS-b-PS with two kinds of chloromethylation agents is carried out. The thermal stability, morphology, and conductivity of the obtained AEBPEs (PFS-b-QAPS(OH)) were investigated by thermogravimetry analysis, differential scanning calorimeter, small-angle X-ray scattering, and AC impedance, respectively.