The multi-scale information among the whole slide images (WSIs) is essential for cancer diagnosis. Although the existing multi-scale vision Transformer has shown its effectiveness for learning multi-scale image representation, it still cannot work well on the gigapixel WSIs due to their extremely large image sizes. To this end, we propose a novel Multi-scale Efficient Graph-Transformer (MEGT) framework for WSI classification. The key idea of MEGT is to adopt two independent efficient Graph-based Transformer (EGT) branches to process the low-resolution and high-resolution patch embeddings (i.e., tokens in a Transformer) of WSIs, respectively, and then fuse these tokens via a multi-scale feature fusion module (MFFM). Specifically, we design an EGT to efficiently learn the local-global information of patch tokens, which integrates the graph representation into Transformer to capture spatial-related information of WSIs. Meanwhile, we propose a novel MFFM to alleviate the semantic gap among different resolution patches during feature fusion, which creates a non-patch token for each branch as an agent to exchange information with another branch by cross-attention mechanism. In addition, to expedite network training, a new token pruning module is developed in EGT to reduce the redundant tokens. Extensive experiments on both TCGA-RCC and CAMELYON16 datasets demonstrate the effectiveness of the proposed MEGT.