The state of health is a crucial state that suggests the capacity of lithium-ion batteries to store and restitute energy at a certain power level, which should be carefully monitored in the battery management system. However, the state of health of batteries is unmeasurable and, currently, it is usually estimated within a specific area of the whole charging data, which is very limited in practical application because of the incomplete and random charging behaviors of users. In this paper, we intend to estimate the state of health of batteries with flexible partial charging curves and normal multi-layer perceptron based on the degradation data of eight 0.74 Ah batteries. To make the estimation more adaptive and flexible, we extract several features from partial charging curves. Analysis of the relationship between extracted features and the state of health shows that the extracted features are useful in estimation. As the length of the partial charging curve increases, the extracted features still function well, and the root mean square error of the test set is lower than 1.5%. Further validation on the other two types of batteries reveals that the proposed method achieves high accuracy even with different sampling and working conditions. The proposed method offers an easy-to-implement way to achieve an accurate estimation of a battery’s state of health.