The risk of disability in older adults with hypertension is substantially high, and prediction of disability risk is crucial for subsequent management. This study aimed to construct prediction models of disability risk for geriatric patients with hypertension at different time intervals, as well as to assess the important predictors and influencing factors of disability. This study collected data from the Chinese Longitudinal Healthy Longevity and Happy Family Study. There were 1576, 1083 and 506 hypertension patients aged 65+ in 2008 who were free of disability at baseline and had completed outcome information in follow-up of 2008-2012, 2008-2014, 2008-2018. We built five machine learning (ML) models to predict the disability risk. The classic statistical logistic regression (classic-LR) and shapley additive explanations (SHAP) was further introduced to explore possible causal factors and interpret the optimal models' decisions. Among the five ML models, logistic regression, extreme gradient boosting, and deep neural network were the optimal models for detecting 4-, 6-, and 10-year disability risk with their AUC-ROCs reached 0.759, 0.728, 0.694 respectively. The classic-LR revealed potential casual factors for disability and the results of SHAP demonstrated important features for risk prediction, reinforcing the trust of decision makers towards black-box models. The optimal models hold promise for screening out hypertensive old adults at high risk of disability to implement further targeted intervention and the identified key factors may be of additional value in analyzing the causal mechanisms of disability, thereby providing basis to practical application.