The graph-based model can help to detect suspicious fraud online. Owing to the development of Graph Neural Networks~(GNNs), prior research work has proposed many GNN-based fraud detection frameworks based on either homogeneous graphs or heterogeneous graphs. These work follow the existing GNN framework by aggregating the neighboring information to learn the node embedding, which lays on the assumption that the neighbors share similar context, features, and relations. However, the inconsistency problem is hardly investigated, i.e., the context inconsistency, feature inconsistency, and relation inconsistency. In this paper, we introduce these inconsistencies and design a new GNN framework, $\mathsf{GraphConsis}$, to tackle the inconsistency problem: (1) for the context inconsistency, we propose to combine the context embeddings with node features, (2) for the feature inconsistency, we design a consistency score to filter the inconsistent neighbors and generate corresponding sampling probability, and (3) for the relation inconsistency, we learn a relation attention weights associated with the sampled nodes. Empirical analysis on four datasets indicates the inconsistency problem is crucial in a fraud detection task. The extensive experiments prove the effectiveness of $\mathsf{GraphConsis}$. We also released a GNN-based fraud detection toolbox with implementations of SOTA models. The code is available at https://github.com/safe-graph/DGFraud.