Lithium-ion batteries are widely used in various fields due to their superior energy storage performance. However, with the increase of using time, the aging of lithium-ion batteries is prone to lead to different failure degrees, so online fault diagnosis for lithium-ion batteries is crucial. To improve the accuracy and transparency of fault diagnosis, this paper proposed a fault diagnosis model based on continuous probability distribution evidential reasoning(ER) rule, and optimized the related parameters by optimization method. Firstly, this paper extracted characteristic indicators that could reflect batteries' state of health(SOH) from charging and discharging process, and used Spearman correlation coefficient to analyze the correlation between characteristic indicators and the SOH to extract health indexes. Secondly, considering the uncertainty of battery fault information, this paper proposed a fault diagnosis method based on continuous probability distribution reference points of evidential reasoning(ER) rule, it used Gaussian distribution to describe the reference points, so as to achieve online fault diagnosis. Thirdly, it designed a whale optimization algorithm(WOA) with constraints to optimize evidence parameters to construct the GER-W fault diagnosis model, so that the accuracy of model fault diagnosis reached the best. Finally, it made fuzzy division of faults by analyzing SOH, and verified the effectiveness of the GER-W model by taking the NASA battery data set as an example. In addition, the model was extended to batteries' SOH estimation. The verification results show that GER-W model has higher accuracy and more transparent process than other fault diagnosis methods, and it also has a certain effect in SOH estimation.