By using the transfer matrix method, the theoretical investigation has been carried out in the near- and mid-infrared bandgaps for a periodic multilayered structure that was composed of superconductor (SC) and semiconductor-metamaterial. It was found that two bandgaps appeared within the computational regions which are effectively optimized by manipulating the thickness of the SC film, fill factor of the semiconductor-metamaterial and the incidence angle of the incident electromagnetic wave. However, the thickness of the SC film and fill factor of the semiconductor-metamaterial are responsible for the red-shift of bandgaps, while the blue-shift is accounted for by the angle of incidence for both transverse electric (TE) and transverse magnetic (TM) waves. It is notable, for the TM wave, that the bandgaps disappeared at the incident angles of approximately 60 degrees. Such properties are quite useful in designing any new types of edge filters and other optical devices in the near- and mid-infrared frequencies.