White blood cells are a core component of the immune system, responsible for protecting the human body from foreign invaders and infectious diseases. A decrease in the white blood cell count can lead to weakened immune function, increasing the risk of infection and illness. However, determining the number of white blood cells usually requires the expertise and effort of radiologists. In recent years, with the development of image processing technology, biomedical systems have widely applied image processing techniques in disease diagnosis. We aim to classify the subtypes of white blood cells using image processing technology. To improve the ability to extract fine information during the feature extraction process, the spatial prior convolutional attention (SPCA) module is proposed. In addition, to enhance the connection between features at distant distances, the Shifted Window (Swin) Transformer network is used as the backbone for feature extraction. The SGTformer network for white blood cell subtype classification is proposed by combining recursive gate convolution and SPCA modules. Our method is validated on the white blood cell dataset, and the experimental results demonstrate an overall accuracy of 99.47% in white blood cell classification, surpassing existing mainstream classification algorithms. It is evident that this method can effectively accomplish the task of white blood cell classification and provide robust support for the health of the immune system.