Neural transducers provide a natural approach to streaming ASR. However, they augment output sequences with blank tokens which leads to challenges for domain adaptation using text data. This paper proposes a label-synchronous neural transducer (LS-Transducer), which extracts a label-level encoder representation before combining it with the prediction network output. Hence blank tokens are no longer needed and the prediction network can be easily adapted using text data. An Auto-regressive Integrate-and-Fire (AIF) mechanism is proposed to generate the label-level encoder representation while retaining the streaming property. In addition, a streaming joint decoding method is designed to improve ASR accuracy. Experiments show that compared to standard neural transducers, the proposed LS-Transducer gave a 10% relative WER reduction (WERR) for intra-domain Librispeech-100h data, as well as 17% and 19% relative WERRs on cross-domain TED-LIUM 2 and AESRC2020 data with an adapted prediction network.