The demand for environmentally friendly types of energy is growing all over the world, which naturally increases the intensity of studies on fuel mixtures that have high contents of hydrogen. In this case, methanol steam reforming is a leading effective research area, as it is a process with low energy consumption. The results of the steam reforming of methanol on synthesized catalysts by the solution combustion synthesis (SCS), self-propagating high-temperature synthesis (SHS), and moisture impregnation capacity methods are presented. A study was conducted to evaluate the activity of Cu-Ce-Al catalysts with varying ratios of components for hydrogen production, comparing the SCS method with the other mentioned methods. The methanol conversion reached 99% and the selectivity of H2 was 88% at 500 °C. The study showed that the replacement of Al3+ ions with Cu2+ and Ce3+ cations leads to the formation of spinels, such as CuAl2O4 and CeAlO3. As a consequence, the CuAl2O4 and CeAlO3 lattice parameters increase because of the difference in the ionic radii of Al3+ (0.53 Å), Cu2+ (0.73 Å), and Ce3+ (1.07 Å). Advantages of SCS catalysts in the process of the steam reforming of methanol have been demonstrated. The goal of this research is to create a new catalyst for methanol’s conversion into hydrogen-containing fuel mixtures, the production of which, in the future, will be a huge step in the transition to more energy-efficient and environmentally friendly methods of their synthesis.