Remote sensing (RS) image classification has attracted much attention recently and is widely used in various fields. Different to natural images, the RS image scenes consist of complex backgrounds and various stochastically arranged objects, thus making it difficult for networks to focus on the target objects in the scene. However, conventional classification methods do not have any special treatment for remote sensing images. In this paper, we propose a two-stream swin transformer network (TSTNet) to address these issues. TSTNet consists of two streams (i.e., original stream and edge stream) which use both the deep features of the original images and the ones from the edges to make predictions. The swin transformer is used as the backbone of each stream given its good performance. In addition, a differentiable edge Sobel operator module (DESOM) is included in the edge stream which can learn the parameters of Sobel operator adaptively and provide more robust edge information that can suppress background noise. Experimental results on three publicly available remote sensing datasets show that our TSTNet achieves superior performance over the state-of-the-art (SOTA) methods.