This paper is devoted to developing a recurrent neural network (RNN) solution for segmenting the unpunctuated transcripts generated by automatic speech recognition for simultaneous interpretation. RNNs are effective in capturing long-distance dependencies and straightforward for online decoding. Thus, they are ideal for the task compared to the conventional n-gram language model (LM) based approaches and recent neural machine translation based approaches. This paper proposes a multishifted RNN to address the trade-off between accuracy and latency, which is one of the key characteristics of the task. Experiments show that our proposed method improves the segmentation accuracy measured in F1 by 21.1% while maintains approximately the same latency, and reduces the BLEU loss to the oracle segmentation by 28.6%, when compared to a strong baseline of the RNN LM-based method. Our online sentence segmentation toolkit is open-sourced 1 to promote the field.