Abstract: Open-vocabulary semantic segmentation strives to distinguish pixels into different semantic groups from an open set of categories. Most existing methods explore utilizing pre-trained vision-language models, in which the key is to adapt the image-level model for pixel-level segmentation task. In this paper, we propose a simple encoder-decoder, named SED, for open-vocabulary semantic segmentation, which comprises a hierarchical encoder-based cost map generation and a gradual fusion decoder with category early rejection. The hierarchical encoder-based cost map generation employs hierarchical backbone, instead of plain transformer, to predict pixel-level image-text cost map. Compared to plain transformer, hierarchical backbone better captures local spatial information and has linear computational complexity with respect to input size. Our gradual fusion decoder employs a top-down structure to combine cost map and the feature maps of different backbone levels for segmentation. To accelerate inference speed, we introduce a category early rejection scheme in the decoder that rejects many no-existing categories at the early layer of decoder, resulting in at most 4.7 times acceleration without accuracy degradation. Experiments are performed on multiple open-vocabulary semantic segmentation datasets, which demonstrates the efficacy of our SED method. When using ConvNeXt-B, our SED method achieves mIoU score of 31.6\% on ADE20K with 150 categories at 82 millisecond ($ms$) per image on a single A6000. Our source code is available at https://github.com/xb534/SED.