Recently in statistical parametric speech synthesis, we proposed a continuous sinusoidal model (CSM) using continuous F0 (contF0) in combination with Maximum Voiced Frequency (MVF), which was successfully giving state-of-the-art vocoders performance (e.g. similar to STRAIGHT) in synthesized speech. In this paper, we address the use of sequence-to-sequence modeling with recurrent neural networks (RNNs). Bidirectional long short-term memory (Bi-LSTM) is investigated and applied using our CSM to model contF0, MVF, and Mel-Generalized Cepstrum (MGC) for more natural sounding synthesized speech. For refining the output of the contF0 estimation, post-processing based on time-warping approach is applied to reduce the unwanted voiced component of the unvoiced speech sounds, resulting in an enhanced contF0 track. The overall conclusion is covered by objective evaluation and subjective listening test, showing that the proposed framework provides satisfactory results in terms of naturalness and intelligibility, and is comparable to the high-quality WORLD model based RNNs.