Dynamic temporal graphs have become essential in developing recommendation systems and social science research. In this study, we introduce a novel approach for a dynamic temporal graph network named Graph of Now and Past Network (GNP), which enhances temporal graph learning by considering the traditional past data as the past and now. The proposed approach simultaneously addresses the issue of data staleness and emphasizes new edge features and active neighbor information within the existing memory structure. GNP supports real-world applications that demand continuous adaptation, offering timely and context-aware predictions by modeling both recent and historical interaction patterns. Extensive experiments have been conducted, and the results reveal that the proposed model outperforms state-of-the-art baselines, including TGN on four public temporal datasets. The results also indicate that GNP demonstrates high stability and rapid convergence during training. The source code is available at https://github.com/for4ever44/GNP .