In this paper, the generation of hydrogen from alkaline sodium borohydride solution by hydrolysis is studied. To obtain catalysts for efficient hydrogen generation, Ni, Mn, Mo, and Co metals were deposited on the Cu surface by the simple electroless metal deposition method using morpholine borane as a reducing agent. Depending on the peculiarities of the deposition of each metal, the coating thickness was ca. 1 μm for all catalysts. The deposited coatings were compact and crack-free, with multilayer characteristics and a cauliflower-like structure. The prepared Ni/Cu, NiMn/Cu, NiMo/Cu, NiCo/Cu, NiCoMn/Cu, NiCoMo/Cu, and NiCoMoMn/Cu catalysts showed an efficient catalytic activity for sodium borohydride hydrolysis reaction. The lowest activation energy of 45.3 kJ mol−1 for sodium borohydride hydrolysis reaction was obtained using the NiCoMoMn/Cu catalyst. The highest hydrogen generation rate of 3.08 mL min−1 was also achieved using this catalyst at 303 K. With a further increase in temperature to 343 K, the hydrogen generation rate catalyzed by the NiCoMoMn/Cu increased 7.7 times and reached 23.57 mL min−1.