Remote-sensing images have complex spatial variability and wide coverage scenarios, but the current remote-sensing scene-classification algorithms cannot easily extract and utilize information effectively. Hence, a network architecture that fuses multiscale hierarchical features (MHFNet) is proposed to solve these problems. First, FasterNet is introduced as a multilevel feature extractor to extract multiple levels of features from remote-sensing scenes. Subsequently, a multiscale interaction transformer (MSIT) is proposed to capture the abundant information of various scales hidden in each level and to model dependencies between remote pixels. Finally, an adaptive token mixer (ATM) is designed to enhance the model's understanding and analysis capabilities of remote-sensing scenes by examining the correlation between hierarchical features and fusing hierarchical features. The accuracy rates of MHFNet on two public remote-sensing datasets, i.e., AID and NWPU-RESISC45, are 98.63% and 95.73% respectively. The classification results show that MHFNet performs better than other classification methods.