The number of battery cells in a large-scale energy storage power station is enormous. The conventional convolutional neural networks achieve high prediction accuracy for battery capacity degradation. However, they have high demand for computational resources, which limits their application in practical battery management systems of energy storage power stations. To solve this problem, this paper proposes a battery capacity degradation prediction method based on a binary neural network. First, a lightweight model is designed by binarizing the network weights and activation functions, using the discharge capacity-voltage curve of the battery as input to output the cumulative distribution function values of key parameters. Subsequently, these parameters are solved using the bisection method and substituted into a hyperbola equation to predict the capacity degradation curve. Finally, experiments are conducted on a public lithium-ion battery dataset. The results show that under the same prediction accuracy as traditional neural network models, the proposed model reduces the number of parameters by 48.9% and improves prediction speed by 22.37%. This study reduces model computational complexity and hardware computational cost and also provides a more efficient and lightweight prediction method for battery management in large-scale energy storage power stations.