The development of green energy technology has necessitated research on methods to recover and reuse spent Li-ion batteries. To increase the recovery efficiency of precious metals from spent Li batteries, the effects of different leaching parameters, such as the temperature, leaching time, leach liquor concentrations, and solid-liquid ratio, on the leaching efficiency of the NH3 + (NH4)2SO4 + Na2SO3 system were systematically investigated in this study. The most suitable leaching conditions were determined as follows: (NH4)2SO4 concentration = 1.5 mol/L, Na2SO3 concentration = 0.5 mol/L, NH3 concentration = 4 mol/L, solid-liquid ratio = 10:1, leaching time = 180 min, and temperature = 90 °C. Under the most suitable conditions, the leaching efficiencies of Li, Co, and Ni were 96.2%, 89.9%, and 90.1%, respectively, and up to 90.8% Mn remained as a leach residue with good crystallinity. The leach residue was characterised using X-ray diffraction, scanning electron microscopy, electron probe microanalysis, and other detection techniques. The kinetic modelling showed that the leaching process of Li, Co, and Ni was controlled by the surface chemical reaction with apparent activation energies of 62.0, 81.5 and 76.3 kJ/mol, for Li, Co and Ni, respectively. Moreover, Mn precipitated as (NH4)2Mn(SO3)2·H2O in the residue where higher leaching temperatures produced residues of better crystallinity. The optimum temperature to obtain a well-crystallised residue was 90 °C.