High-dimensional semi-competing risks data consisting of two probably correlated events, namely terminal event and non-terminal event, arise commonly in many biomedical studies. However, the corresponding statistical analysis is rarely investigated. A joint model-free feature screening procedure for both terminal and non-terminal events is proposed, which could allow the associated covariates to be in an ultra-high dimensional feature space. The joint screening utility is constructed from distance correlation between each predictor’s survival function and joint survival function of terminal and non-terminal events. Under rather mild technical assumptions, it is demonstrated that the proposed joint feature screening procedure enjoys sure screening and consistency in ranking properties. An adaptive threshold rule is further suggested to simultaneously identify important covariates and determine number of these covariates. Extensive numerical studies are conducted to examine the finite-sample performance of the proposed methods. Lastly, the suggested joint feature screening procedure is illustrated through a real example.