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In real-world scenarios, the recognition of unknown activities poses a significant challenge for group activity recognition. Existing methods primarily focus on closed sets, leaving the task of open set group activity recognition unexplored. In this paper, we introduce the concept of open set group activity recognition for the first time and propose a novel recognition framework to deal with it. To mitigate potential scene biases, keypoints extracted from groups are utilized as input. Our framework employs a two-stage approach: Evidence Aware Collection and Evidence Aware Decision, to address the challenge of insufficient evidence for rejecting unknown classes. Specifically, encoders are established at the individual, subgroup, and group scales to collect activity evidence among group members. By applying an attention mechanism, we focus on important evidence, resulting in a set of aggregated evidence. The uncertainty estimated from evidence is then used to effectively distinguish between known and unknown classes. Additionally, we perform open set splits on two publicly available group activity recognition datasets. Experimental results demonstrate that our method shows promising performance in open set group activity recognition while maintaining comparable performance under closed set conditions.