Battery state-of-health (SOH) estimation is an effective approach to evaluate battery reliability and reduce maintenance costs for battery-based backup power supply systems. This paper proposes a novel SOH estimation method for batteries, which only uses the response characteristics of load surges and is, therefore, non-destructive to the estimated battery and its system. The discrete wavelet transform (DWT) method based on multi-resolution analysis (MRA) is used for wavelet energy features extraction, and the fuzzy cerebellar model neural network (FCMNN) is introduced to design the battery SOH estimator. The response voltage signals to load surges are used in the training and detection process of the FCMNN. Compared to conventional methods, the proposed method only exploits characteristics of online response signals to the inrush currents rather than injecting interference signals into the battery. The effectiveness of the proposed method is validated by detailed simulation analysis and experiments.