Traffic forecasting is a fundamental problem in intelligent transportation systems. Existing traffic predictors are limited by their expressive power to model the complex spatial-temporal dependencies in traffic data, mainly due to the following limitations. Firstly, most approaches are primarily designed to model the local shared patterns, which makes them insufficient to capture the specific patterns associated with each node globally. Hence, they fail to learn each node's unique properties and diversified patterns. Secondly, most existing approaches struggle to accurately model both short- and long-term dependencies simultaneously. In this paper, we propose a novel traffic predictor, named Meta Attentive Graph Convolutional Recurrent Network (MAGCRN). MAGCRN utilizes a Graph Convolutional Recurrent Network (GCRN) as a core module to model local dependencies and improves its operation with two novel modules: 1) a Node-Specific Meta Pattern Learning (NMPL) module to capture node-specific patterns globally and 2) a Node Attention Weight Generation Module (NAWG) module to capture short- and long-term dependencies by connecting the node-specific features with the ones learned initially at each time step during GCRN operation. Experiments on six real-world traffic datasets demonstrate that NMPL and NAWG together enable MAGCRN to outperform state-of-the-art baselines on both short- and long-term predictions.