The present invention provides a polymer composite membrane having a polymer membrane and a poly(furfuryl alcohol) filling internal pores of the polymer membrane. The polymer composite membrane can have a high proton conductivity and/or a reduced methanol permeability and can be used in fuel cells, electrochemical sensor, and the like. The present invention also provides a method of making a polymer composite membrane, by providing a perfluorosulfonic polymer member, subjecting the perfluorosulfonic polymer member to a furan-based monomer, and polymerizing the furan-based monomer to obtain a polymer composite membrane having a high proton conductivity and/or a reduced methanol permeability.