Recent years, convolutional neural networks (CNNs) have attracted attention in the research of hyperspectral image (HSI) unmixing, but still calling for complementary approaches to process global information. Consequently, a few transformer-based unmixing networks have been developed. To enhance the richness and diversity of features, a network called SSLT-Net is proposed, which is the combination of CNN and linear transformer. This network capably extracts local, global, spatial, and spectral features of the HSI, enabling it to accomplish an optimized fusion of these four diverse characteristics. It comprises three pivotal modules: a grouped multiscale convolution module encodes low-level features from different receptive fields. Then, an LSTransformer module is proposed, which is a linear transformer with a shuffle attention (SA) block used to extract global spatial and spectral features of images. Finally, a MaxPoolformer module is designed to utilize max pooling to strengthen local features. The above two modules are connected in parallel to form a dual branch structure to encode deeper composite features. By comparing with six methods on three real datasets (Apex, Samson, and Jasper Ridge), the proposed network has showcased its formidable potential and distinct advantages in tackling hyperspectral unmixing tasks. The experimental results indicate that it is crucial to extract and fuse various features (local and global and spectral and spatial) in hyperspectral unmixing tasks. The code is available at https://github.com/ HyperSystemAndImageProc/HyperspectrlUnmixing-SSLTNet.