The causality relation modeling remains a challenging task for group activity recognition. The causality relations describe the influence of some actors (cause actors) on other actors (effect actors). Most existing graph models focus on learning the actor relation with synchronous temporal features, which is insufficient to deal with the causality relation with asynchronous temporal features. In this paper, we propose an Actor-Centric Causality Graph Model, which learns the asynchronous temporal causality relation with three modules, i.e., an asynchronous temporal causality relation detection module, a causality feature fusion module, and a causality relation graph inference module. First, given a centric actor and correlative actor, we analyze their influences to detect causality relation. We estimate the self influence of the centric actor with self regression. We estimate the correlative influence from the correlative actor to the centric actor with correlative regression, which uses asynchronous features at different timestamps. Second, we synchronize the two action features by estimating the temporal delay between the cause action and the effect action. The synchronized features are used to enhance the feature of the effect action with a channel-wise fusion. Third, we describe the nodes (actors) with causality features and learn the edges by fusing the causality relation with the appearance relation and distance relation. The causality relation graph inference provides crucial features of effect action, which are complementary to the base model using synchronous relation inference. The two relation inferences are aggregated to enhance group relation learning. Extensive experiments show that our method achieves state-of-the-art performance on the Volleyball dataset and Collective Activity dataset.