The increasing pervasiveness of object tracking technologies leads to huge volumes of spatiotemporal data collected in the form of trajectory streams. The discovery of useful group patterns from moving objects' movement behaviours in trajectory streams is critical for real-time applications ranging from transportation management to military surveillance. Motivated by this, we first propose a novel pattern, called evolving group, which models the unusual group events of moving objects that travel together within density connected clusters in evolving streaming trajectories. Our theoretical analysis and empirical study on the Osaka Pedestrian data and Beijing Taxi data demonstrate its effectiveness in capturing the development, evolution, and trend of group events of moving objects in streaming context. Moreover, we propose a discovery method that efficiently supports online detection of evolving groups over massive-scale trajectory streams using a sliding window. It contains three phases along with a set of novel optimization techniques designed to minimize the computation costs. Furthermore, to scale to huge workloads over evolving streams, we extend our discovery method to a parallel framework by using a sector-based partition. Our comprehensive empirical study demonstrates that our online discovery framework is effective and efficient on real-world high-volume trajectory streams.