This paper presents a study of using deep bidirectional long short-term memory (DBLSTM) as acoustic model for DBLSTM-HMM based large vocabulary continuous speech recognition (LVCSR), where a context-sensitive-chunk (CSC) backpropagation through time (BPTT) approach is used to train DBLSTM by splitting each training sequence into chunks with appended contextual observations, and a (possibly overlapped) CSCs based decoding method is used for recognition. Our approach makes mini-batch based training on GPU more efficient and reduces the latency of DBLSTM-based LVCSR from a whole utterance to a short chunk. Evaluations have been made on Switchboard-I benchmark task. In comparison with epochwise BPTT training, our method can achieve about three times speed-up on a single GPU card. In comparison with a highly optimized DNN-HMM system trained by a frame-level cross entropy (CE) criterion, our CE-trained DBLSTM-HMM system achieves relative word error rate reductions of 9% and 5% on Eval2000 and RT03S testing sets, respectively.