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In recent years, deep learning (DL)-based methods have been widely used in code vulnerability detection. The DL-based methods typically extract structural information from source code, e.g., code structure graph, and adopt neural networks such as Graph Neural Networks (GNNs) to learn the graph representations. However, these methods fail to consider the heterogeneous relations in the code structure graph, i.e., the heterogeneous relations mean that the different types of edges connect different types of nodes in the graph, which may obstruct the graph representation learning. Besides, these methods are limited in capturing long-range dependencies due to the deep levels in the code structure graph. In this paper, we propose a Meta-path based Attentional Graph learning model for code vulNErability deTection, called MAGNET. MAGNET constructs a multi-granularity meta-path graph for each code snippet, in which the heterogeneous relations are denoted as meta-paths to represent the structural information. A meta-path based hierarchical attentional graph neural network is also proposed to capture the relations between distant nodes in the graph. We evaluate MAGNET on three public datasets and the results show that MAGNET outperforms the best baseline method in terms of F1 score by 6.32%, 21.50%, and 25.40%, respectively. MAGNET also achieves the best performance among all the baseline methods in detecting Top-25 most dangerous Common Weakness Enumerations (CWEs), further demonstrating its effectiveness in vulnerability detection.