In this study, tartaric acid was used to extract the valuable metals lithium (Li), cobalt (Co), nickel (Ni), and manganese (Mn) from the anodes of waste Li-ion batteries. The effects of various factors, namely, acid concentration, the amount of the reducing agent added, temperature, solid-to-liquid (S/L) ratio, and time, on leaching efficiency were explored in order to determine the best conditions for metal recovery. First, Taguchi methods were used to obtain the initial parameters and the factor weights affecting leaching efficiency. Finally, the optimal leaching parameters were obtained through confirmation experiment. For optimal leaching rates, the acid concentration was 2 mol L−1, the time was 30 min, the S/L ratio was 10 g L−1, the temperature was 90 ℃, and the amount of hydrogen peroxide (H2O2) added was 1.0 vol.%, resulting in leaching efficiencies of Li, Co, Ni, and Mn of 87.29, 80.51, 95.78, and 99.99%, respectively. The valuable metal Co can be used as a sensor material.