This paper proposes a deep auto-encoder structure to extract robust spectral features for statistical parametric speech synthesis. The technique allows us to compress the low-dimensional features from high dimensional spectral envelope without degradation for full-band speech in a data-driven way. We carried out a subjective evaluation and found that the optimum auto-encoder architecture. Experimental results showed that an analysis-by-synthesis using the proposed auto-encoder has lower reconstruction error of spectral envelope than conventional mel-cepstral analysis in narrow-band as well as full-band. Our results confirm that the proposed method increases the quality of synthesized speech in text-to-speech experiments.