In this paper, the control theory is applied to assist the estimation of state of health (SoH) which is a key parameter to battery management. Battery can be treated as a system, and the internal state, e.g. SoH, can be observed through certain system output data. Based on the philosophy of human health and athletic ability estimation, variables from a specific process, which is a constant current charge subprocess, are obtained to depict battery SoH. These variables are selected according to the differential geometric analysis of battery terminal voltage curves. Moreover, the relationship between the differential geometric properties and battery SoH is modelled by the group method of data handling (GMDH) polynomial neural network. Thus, battery SoH can be estimated by GMDH with inputs of voltage curve properties. Experiments have been conducted on different types of Li-ion battery, and the results show that the proposed method is valid for SoH estimation.