In this study, the catalytic activities of the steam methane reforming (SMR) reactions with two catalysts, including nickel–scandia-stabilized zirconia (Ni–SSZ) and copper/nickel–scandia-stabilized zirconia (Cu/Ni–SSZ), were examined and compared. The microstructure and crystallinity of the as-prepared catalysts were characterized by scanning electron microscopy, Raman spectroscopy, and X-ray diffraction. Mass spectrometer was applied in the outlet streams, in order to simultaneously monitor the time-dependent kinetics in the reactor for an activity test and conversion examination. Finally, thermogravimetric analysis (TGA) and Raman spectrometer were implemented for further verification of carbon residuals on the catalysts. It was found that the incorporation of Cu on Ni–SSZ imposed significant constraints on the growth of nickel crystallites from NiO during the annealing process in reducing atmospheres. The methane conversion of Ni–SSZ and Cu/Ni–SSZ catalysts (annealed at 300 °C for 2 h) was 36.2 and 26.0%, respectively. However, the amount of carbon residuals on Cu/Ni–SSZ catalyst (300 °C for 2 h) was 18.6%, which is lower than that of the Ni–SSZ catalysts (33.2%) from TGA results. Further Raman experiments revealed that more graphite-like carbon residuals and less defects or amorphous carbons (IG/ID = 2.0) were found in the case of Cu/Ni–SSZ catalysts (300 °C for 2 h). Among the catalysts in this study, the Cu/Ni–SSZ catalyst (300 °C for 2 h) is considered as a promising catalyst for SMR reaction, since it has a fair methane conversion, and characterized higher CO2 selectivity and lower CO selectivity without compromising the hydrogen purity. More importantly, the least amount of carbon residuals was found in Cu/Ni–SSZ catalyst (300 °C for 2 h), which assured a better lifetime.