Accurate capacity estimation of lithium-ion battery packs is crucial for health management and safe operation. The existing methods cannot reflect the variation of capacity distribution with service time. Addressing this problem a heteroscedastic Gaussian process regression (HGPR) model is developed. Different from the standard Gaussian process regression which assumes homoscedasticity variation of the output noise, the HGPR constructs a new Gaussian process to represent the output noise with service time-related variance. The model employs charging data from electric vehicle battery packs to construct training and testing sets, selects inputs through capacity correlation analysis, and employs variational approximation for HGPR hyperparameter optimization. Experimental results demonstrate that HGPR not only achieves higher accuracy in mean capacity estimation compared to Gaussian process regression and neural networks, but also effectively captures the increasing trend of capacity standard deviation over time and improves the interval coverage rate of the estimated distribution. Further analysis reveals the distinct roles of the two Gaussian processes in HGPR for mean and standard deviation estimation, and investigates the influence of different feature combinations and kernel functions on estimation accuracy. This research provides a valuable reference for uncertainty modeling in battery pack capacity and health assessment.