The state of health (SOH) and remaining useful life (RUL) of a battery are key indicators for measuring battery performance degradation and remaining useful time. Predicting battery SOH and RUL is of great importance in practical applications. Usually, battery operation data is used to train machine learning algorithms, such as neural networks or deep learning, to capture the changing patterns of battery SOH and RUL and make predictions. Traditional machine learning models often use a single model to adapt to the entire dataset, which is inadequate when dealing with complex and highly heterogeneous data. Building a model for each prediction target incurs high training and maintenance costs. Sparse mixture of experts (SMoE) was used to construct a joint prediction model for battery SOH and RUL, and battery fusion data was used to simultaneously predict battery SOH and RUL. The results of testing on NASA's public dataset show that the proposed joint prediction model can effectively predict battery SOH and RUL, with a mean square error of 0.069 for SOH prediction and 2.042 for RUL prediction. Tested on the EIS public dataset, the mean square error of the SOH prediction value of the joint prediction model was 0.118, and the mean square error of the RUL prediction value was 3.072, indicating a significant improvement in accuracy. The models and methods proposed in the text have certain reference and application value.