The band characteristics and the phase shift of electromagnetic waves in one-dimensional (1D) Fibonacci photonic structures composed of subwavelength nano-scale C_(60) fullerene and tellurium thin films are investigated theoretically in detail for both the TE and TM polarizations for different incident angles. We adopt the transmission matrix method to analyze the transmission properties of the supposed subwavelength structure. We observe that within the stop band the reflection phase difference changes smoothly and increases with increasing incident angle. In the center of the gap the reflection phase difference remains almost unchanged in a broad wavelength band. Especially, at both the edges of the gap, the reflection phase difference remains zero in spite of the change of the incident angle. Based on our results, the supposed structure provides a convenient way to design very compact phase retarders.