Session-based recommendation plays an important role in daily life and exists in many scenarios, such as online shopping websites and streaming media platforms. Recently, some works have focused on using graph neural networks (GNNs) to recommend new items in session-based scenarios. However, these methods have encountered several limitations. First, existing methods typically ignore the impact of items’ visited time in constructing session graphs, resulting in a departure from real-world recommendation dynamics. Second, sessions are often sparse, making it challenging for GNNs to learn valuable item embedding and user preferences. Third, the existing methods usually overemphasize the impact of the last item on user preferences, neglecting their interest in multiple items in a session. To address these issues, we introduce a time-sensitive graph neural network for new item recommendation in session-based scenarios, namely, TSGNN. Specifically, TSGNN provides a novel time-sensitive session graph constructing technique to solve the first problem. For the second problem, TSGNN introduces graph augmentation and contrastive learning into it. To solve the third problem, TSGNN designs a time-aware attention mechanism to accurately discern user preferences. By evaluating the compatibility between user preferences and candidate new item embeddings, our method recommends items with high relevance scores for users. Comparative experiments demonstrate the superiority of TSGNN over state-of-the-art (SOTA) methods.