Attention-based models have made tremendous progress on end-to-end automatic speech recognition(ASR) recently. However, the conventional transformer-based approaches usually generate the recognition sequence token by token from left to right, leaving the right-to-left contexts unexploited. In this work, we introduce a synchronous bidirectional speech transformer to utilize the different directional contexts simultaneously. Speciﬁcally, the outputs of our proposed transformer include a left-to-right target, and a right-to-left target. In inference stage, we use the introduced bidirectional beam search method, which can not only generate left-to-right candidates but also generate right-to-left candidates, and determine the best hypothesis sentence by scores. To demonstrate our proposed speech transformer with a bidirectional decoder(STBD), we conduct extensive experiments on the AISHELL-1 dataset. The results of experiments show that STBD achieves a 3.6% relative CER reduction(CERR) over the unidirectional speech transformer baseline, and the strongest model in this paper called STBD-Big model can achieve 6.64% CER on the test set, without language model rescoring and any extra data augmentation strategies.