Machine learning methods are expected to play a significant role in battery state of charge (SOH) estimation, leveraging their strengths in self-learning and nonlinear fitting. One of the key challenges in SOH estimation is the concept drift issue, which refers to changes in the data distribution between the training and test datasets. General machine learning methods assume that the training data shares similar characteristics with the test data. However, in SOH estimation tasks, differences in the environment and the characteristics of the battery itself can cause concept drift, which then impacts the model's effectiveness. As a result, many data-driven models that perform well in laboratory conditions struggle to be applied to other target batteries. This is a common and significant battery diagnosis technology issue, yet it remains unresolved. This paper proposes a multi-domain transfer Gaussian process regression (MTR-GPR) SOH estimation approach to address this issue. In this model, training data do not directly participate in the model's learning process. Instead, the MTR-GPR model extracts information from different datasets based on the distribution similarity. This method can fully use multi-source battery ageing data while reducing the negative impact of distribution differences. Experimental results prove that MTR-GPR can make reliable SOH estimates with only 20% of target battery data. On the other hand, this method can provide the posterior probability distribution of the prediction results.