An efficient, flexible multi-band thermal emitter is proposed in the present work, consisting of a one-dimensional quasi-periodic photonic crystal and a reflective substrate. All the materials involved in the design have good high-temperature stability. Compared to absorbers with complex shapes, our planar devices are easier to fabricate, lithography-free, large-scale, and cost-effective fabrication. It is found that more and narrower absorption peaks will be generated when more layers of the quasi-periodic photonic crystal composite layer are placed on the top of the metal substrate. All three absorption peaks have the absorbance of more than 97% for the three-cell device we designed. Since the designed emitter has excellent substrate adaptability and is insensitive to polarization and incident angle, it is favourable to fabricate on flexible substrates. The present work may find promising applications in high-temperature and flexibility research areas such as infrared detection.