This paper presents a new hybrid approach for polyphonic Sound Event Detection (SED) which incorporates a temporal structure modeling technique based on a hidden Markov model (HMM) with a frame-by-frame detection method based on a bidirectional long short-term memory (BLSTM) recurrent neural network (RNN). The proposed BLSTM-HMM hybrid system makes it possible to model sound event-dependent temporal structures and also to perform sequence-by-sequence detection without having to resort to thresholding such as in the conventional frame-by-frame methods. Furthermore, to effectively reduce insertion errors of sound events, which often occurs under noisy conditions, we additionally implement a binary mask post-processing using a sound activity detection (SAD) network to identify segments with any sound event activity. We conduct an experiment using the DCASE 2016 task 2 dataset to compare our proposed method with typical conventional methods, such as non-negative matrix factorization (NMF) and a standard BLSTM-RNN. Our proposed method outperforms the conventional methods and achieves an F1-score 74.9 % (error rate of 44.7 %) on the event-based evaluation, and an F1-score of 80.5 % (error rate of 33.8 %) on the segment-based evaluation, most of which also outperforms the best reported result in the DCASE 2016 task 2 challenge.