State-of-the-art Graph Neural Networks (GNNs) have achieved tremendous success in social event detection tasks when restricted to a closed set of events. However, considering the large amount of data needed for training a neural network and the limited ability of a neural network in handling previously unknown data, it remains a challenge for existing GNN-based methods to operate in an open set setting. To address this problem, we design a Quality-aware Self-improving Graph Neural Network (QSGNN) which extends the knowledge from known to unknown by leveraging the best of known samples and reliable knowledge transfer. Specifically, to fully exploit the labeled data, we propose a novel supervised pairwise loss with an additional orthogonal inter-class relation constraint to train the backbone GNN encoder. The learnt, already-known events further serve as strong reference bases for the unknown ones, which greatly prompts knowledge acquisition and transfer. When the model is generalized to unknown data, to ensure the effectiveness and reliability, we further leverage the reference similarity distribution vectors for pseudo pairwise label generation, selection and quality assessment. Following the diversity principle of active learning, our method selects diverse pair samples with the generated pseudo labels to fine-tune the GNN encoder. Besides, we propose a novel quality-guided optimization in which the contributions of pseudo labels are weighted based on consistency. We thoroughly evaluate our model on two large real-world social event datasets. Experiments demonstrate that our model achieves state-of-the-art results and extends well to unknown events.