Heterogeneous treatment effect (HTE) estimation is vital for understanding the change of treatment effect across individuals or subgroups. Most existing HTE estimation methods focus on addressing selection bias induced by imbalanced distributions of confounders between treated and control units, but ignore distribution shifts across populations. Thereby, their applicability has been limited to the in-distribution (ID) population, which shares a similar distribution with the training dataset. In real-world applications, where population distributions are subject to continuous changes, there is an urgent need for stable HTE estimation across out-of-distribution (OOD) populations, which, however, remains an open problem. As pioneers in resolving this problem, we propose a novel Stable Balanced Representation Learning with Hierarchical-Attention Paradigm (SBRL-HAP) framework, which consists of 1) Balancing Regularizer for eliminating selection bias, 2) Independence Regularizer for addressing the distribution shift issue, 3) Hierarchical-Attention Paradigm for coordination between balance and independence. In this way, SBRL-HAP regresses counterfactual outcomes using ID data, while ensuring the resulting HTE estimation can be successfully generalized to out-of-distribution scenarios, thereby enhancing the model's applicability in real-world settings. Extensive experiments conducted on synthetic and real-world datasets demonstrate the effectiveness of our SBRL-HAP in achieving stable HTE estimation across OOD populations, with an average 10% reduction in the error metric PEHE and 11% decrease in the ATE bias, compared to the SOTA methods.