Backprojection networks have achieved promising super-resolution performance for nature images but not well be explored in the remote sensing image super-resolution (RSISR) field due to the high computation costs. In this paper, we propose a Multi-granularity Backprojection Transformer termed MBT for RSISR. MBT incorporates the backprojection learning strategy into a Transformer framework. It consists of Scale-aware Backprojection-based Transformer Layers (SPTLs) for scale-aware low-resolution feature learning and Context-aware Backprojection-based Transformer Blocks (CPTBs) for hierarchical feature learning. A backprojection-based reconstruction module (PRM) is also introduced to enhance the hierarchical features for image reconstruction. MBT stands out by efficiently learning low-resolution features without excessive modules for high-resolution processing, resulting in lower computational resources. Experiment results on UCMerced and AID datasets demonstrate that MBT obtains state-of-the-art results compared to other leading methods.