Abstract: Radiology report generation can automatically generate clinical descriptions from X-ray images, thereby significantly improving the efficiency of radiologists. This task is challenging because it requires medical knowledge to accurately identify diseases and describe them in a professional manner. However, existing methods often overlook the importance of enhancing medical knowledge in describing pivotal areas, a capability that requires models to effectively extract and aggregate knowledge at multiple levels of granularity. Accordingly, we herein propose a novel and compact Efficient Multi-Granularity Knowledge Transfer (\textbf{EMGKT}) method to address the above issues. First, we encode global knowledge embeddings using a medical vision-language model, which provides contextual medical knowledge. Moreover, we devise a novel Fine-Grained Knowledge Distillation (FGKD) training task which efficiently extract fine-grained knowledge. Specifically, the FGKD training task contains teacher embeddings and student embeddings. Teacher embeddings are encoded using extra priors; while student embeddings are learned from the teacher embeddings through knowledge distillation. During inference, the student embeddings are used to enhance fine-grained knowledge while the teacher embeddings are discarded, resulting in negligible computational costs and no need for extra priors. Finally, we further develop a mixture of disease diagnosis expert classifiers to enhance knowledge extraction. The classifiers are initialized using disease embeddings and are modeled as different experts to address various granularity features. Notably, \textbf{EMGKT} can be efficiently applied to most existing methods. Extensive experiments are conducted on two widely-used public datasets and various baselines, which demonstrates the effectiveness and transferability of \textbf{EMGKT}.