Accurate state-of-health (SOH) estimation is critical for the performance and safety of lithium-ion batteries. An innovative method for SOH estimation is proposed by employing a variational quantum algorithm to optimize a stacking integrated learning strategy. The strategy effectively combines multiple model advantages, enhancing the estimation accuracy and generalizability. Using this method, eight sets of health factors are extracted, focusing on the relationship between battery capacity degradation and electrothermal parameters. A stacking integrated learning framework is developed by utilizing diverse primary learners to effectively capture the dynamic changes in health factors. A ridge regression meta-learner is incorporated to address overfitting problems found in primary learners. A significant innovation is the integration of a variational quantum circuit module as the primary learner. This module plays a crucial role in optimizing the hyperparameters for the analysis of complex and high-dimensional battery data. The effectiveness of the method is validated using four different types of batteries, showing a 77.4% improvement in prediction accuracy compared with traditional methods, with the SOH estimation error maintained within a tight margin of 0.67%. The mean absolute error, mean absolute percentage error, and root mean square error with maximum reduction rates are 76.7%, 77.4%, and 62.7%, respectively. The maximum increase in the R-squared coefficient is 5.3%. This study demonstrates the potential of variational quantum algorithms in enhancing the SOH estimation accuracy and opens new possibilities for the advanced health status management of lithium-ion batteries.