The task of Group Activity Recognition (GAR) aims to predict the activity category of the group by learning the actor spatial-temporal interaction relation in the group. Therefore, an effective actor relation learning method is crucial for the GAR task. The previous works mainly learn the interaction relation by the well-designed GCNs or Transformers. For example, to infer the actor interaction relation, GCNs need a learnable adjacency, and Transformers need to calculate the self-attention. Although the above methods can model the interaction relation effectively, they also increase the complexity of the model (the number of parameters and computations). In this paper, we design a novel MLP-based method for Actor Interaction Relation learning (MLP-AIR) in GAR. Compared with GCNs and Transformers, our method has a competitive but conceptually and technically simple alternative, significantly reducing the complexity. Specifically, MLP-AIR includes three sub-modules: MLP-based Spatial relation modeling module (MLP-S), MLP-based Temporal relation modeling module (MLP-T), and MLP-based Relation refining module (MLP-R). MLP-S is used to model the spatial relation between different actors in each frame. MLP-T is used to model the temporal relation between different frames for each actor. MLP-R is used further to refine the relation between different dimensions of relation features to improve the feature's expression ability. To evaluate the MLP-AIR, we conduct extensive experiments on two widely used benchmarks, including the Volleyball and Collective Activity datasets. Experimental results demonstrate that MLP-AIR can get competitive results but with low complexity.