The early fault detection and reliable operation of lithium-ion batteries are two of the main challenges the technology faces. Here, we report a new methodology for early failure detection in lithium-ion batteries. This new methodology is based on wavelet spectral analysis to detect overcharge failure in batteries that is performed for voltage data obtained in cycling tests, subjected to a standard charge/discharge protocol. The main frequencies of the voltage temporal signal, the harmonic components in the regular cycling test, and a low frequency pattern were identified. For the first time, battery failure can be anticipated by wavelet spectral analysis. These results could be the key to the new early detection of battery failures in order to reduce out-of-control explosions and fire risks.