A series of composite proton-exchange membranes have been prepared via sol-gel modification of commercial Nafion membranes with [N-(2-aminoethyl)-3-aminopropyl]trimethoxysilane. The structure and physico-chemical properties (water uptake, ion-exchange capacity, vanadyl ion permeability, and proton conductivity) of the prepared composite membranes have been studied as a function of the precursor loading (degree of the membrane modification). If the amount of the precursor is below 0.4/1 M ratio of the amino groups of the precursor to the sulfonic groups of Nafion, the composite membranes exhibit decreased vanadium ion permeability while having relatively high proton conductivity. With respect to the use of a non-modified Nafion membrane, the performance of the composite membrane with an optimum precursor loading in a single-cell vanadium redox flow battery demonstrates enhanced energy efficiency in 20–80 mA cm−2 current density range. The maximum efficiency increase of 8% is observed at low current densities.