The direction of human gaze is an important indicator of human behavior, reflecting the level of attention and cognitive state towards various visual stimuli in the environment. Convolutional neural networks have achieved good performance in gaze estimation tasks, but their global modeling capability is limited, making it difficult to further improve prediction performance. In recent years, transformer models have been introduced for gaze estimation and have achieved state-of-the-art performance. However, their slicing-and-mapping mechanism for processing local image patches can compromise local spatial information. Moreover, the single down-sampling rate and fixed-size tokens are not suitable for multiscale feature learning in gaze estimation tasks. To overcome these limitations, this study introduces a Swin Transformer for gaze estimation and designs two network architectures: a pure Swin Transformer gaze estimation model (SwinT-GE) and a hybrid gaze estimation model that combines convolutional structures with SwinT-GE (Res-Swin-GE). SwinT-GE uses the tiny version of the Swin Transformer for gaze estimation. Res-Swin-GE replaces the slicing-and-mapping mechanism of SwinT-GE with convolutional structures. Experimental results demonstrate that Res-Swin-GE significantly outperforms SwinT-GE, exhibiting strong competitiveness on the MpiiFaceGaze dataset and achieving a 7.5% performance improvement over existing state-of-the-art methods on the Eyediap dataset.