White blood cells (WBC) play an effective role in the body’s defense against parasites, viruses, and bacteria in the human body. Also, WBCs are categorized based on their morphological structures into various subgroups. The number of these WBC types in the blood of non-diseased and diseased people is different. Thus, the study of WBC classification is quite significant for medical diagnosis. Due to the widespread use of deep learning in medical image analysis in recent years, it has also been used in WBC classification. Moreover, the ConvMixer and Swin transformer models, recently introduced, have garnered significant success by attaining efficient long contextual characteristics. Based on this, a new multipath hybrid network is proposed for WBC classification by using ConvMixer and Swin transformer. This proposed model is called Swin Transformer and ConvMixer based Multipath mixer (SC-MP-Mixer). In the SC-MP-Mixer model, firstly, features with strong spatial details are extracted with the ConvMixer. Then Swin transformer effectively handle these features with self-attention mechanism. In addition, the ConvMixer and Swin transformer blocks consist of a multipath structure to obtain better patch representations in the SC-MP-Mixer. To test the performance of the SC-MP-Mixer, experiments were performed on three WBC datasets with 4 (BCCD), 8 (PBC) and 5 (Raabin) classes. The experimental studies resulted in an accuracy of 99.65% for PBC, 98.68% for Raabin, and 95.66% for BCCD. When compared with the studies in the literature and the state-of-the-art models, it was seen that the SC-MP-Mixer had more effective classification results.