Sound event detection (SED) has gained increasing attention with its wide application in surveillance, video indexing, etc. Existing models in SED mainly generate frame-level prediction, converting it into a sequence multi-label classification problem. A critical issue with the frame-based model is that it pursues the best frame-level prediction rather than the best event-level prediction. Besides, it needs post-processing and cannot be trained in an end-to-end way. This paper firstly presents the one-dimensional Detection Transformer (1D-DETR), inspired by Detection Transformer for image object detection. Furthermore, given the characteristics of SED, the audio query branch and a one-to-many matching strategy for fine-tuning the model are added to 1D-DETR to form Sound Event Detection Transformer (SEDT). To our knowledge, SEDT is the first event-based and end-to-end SED model. Experiments are conducted on the URBAN-SED dataset and the DCASE2019 Task4 dataset, and both show that SEDT can achieve competitive performance.