This paper studies LiFePO4 (LFP) battery capacity fading diversity among different cells with same type and specification under same working states during their whole life cycle; and with consideration of this phenomenon, a novel battery state of health (SOH) estimation method with adaptability to capacity fading diversity is proposed. In order to cope with this capacity fading diversity, a machine learning structure involving a sparse auto-encoder (SAE) and a backward propagation neural network (BPNN) is designed for battery SOH estimation. In this strategy, battery terminal voltage during the later stage of charging process is used as input of SAE; through the reconstruction of input signal, compressive feature of battery voltage is abstracted by SAE; then this compressive feature is used as the input signal of BPNN, and through nonlinear mapping of the neural network, battery SOH can be finally obtained. In this way, a relationship between the battery voltage information at its later charging stage and its SOH can be established. Verification tests show that this SAE-BPNN based SOH estimation strategy possesses a good accuracy with adaptability to the capacity fading diversity and voltage differences among different battery cells, the SOH estimation error can be restrained within the range of +/- 5%, and it is also very convenient to adopt this method in real online battery management system (BMS).