To investigate the effect of acidic nanoparticles on proton conductivity, permeability, and fuel-cell performance, a commercial Nafion® 117 membrane was impregnated with zirconium phosphates (ZrP) and sulfated zirconium (S-ZrO2) nanoparticles. As they are more stable than other solid superacids, sulfated metal oxides have been the subject of intensive research. Meanwhile, hydrophilic, proton-conducting inorganic acids such as zirconium phosphate (ZrP) have been used to modify the Nafion® membrane due to their hydrophilic nature, proton-conducting material, very low toxicity, low cost, and stability in a hydrogen/oxygen atmosphere. A tensile test, water uptake, methanol crossover, Fourier-transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), thermal gravimetric analysis (TGA), and scanning electron microscopy (SEM) were used to assess the capacity of nanocomposite membranes to function in a fuel cell. The modified Nafion® membrane had a higher water uptake and a lower water content angle than the commercial Nafion® 117 membrane, indicating that it has a greater impact on conductivity. Under strain rates of 40, 30, and 20 mm/min, the nanocomposite membranes demonstrated more stable thermal deterioration and higher mechanical strength, which offers tremendous promise for fuel-cell applications. When compared to 0.113 S/cm and 0.013 S/cm, respectively, of commercial Nafion® 117 and Nafion® ZrP membranes, the modified Nafion® membrane with ammonia sulphate acid had the highest proton conductivity of 7.891 S/cm. When tested using a direct single-cell methanol fuel cell, it also had the highest power density of 183 mW cm−2 which is better than commercial Nafion® 117 and Nafion® ZrP membranes.