In this work, we numerically demonstrated a single narrow band THz absorber based on cylindrically shaped periodical p-type doped silicon with excellent attributes, including polarization insensitivity and optical tunability. Good absorption characteristics were demonstrated at 0.57 THz with an absorption of nearly 99.75% and a quality factor of 11.278. Furthermore, its absorbance could be flexibly tuned from above 99% to less than 35% by changing the pump beam fluence from 0 µJ/cm2 to 3000 µJ/cm2. The demonstrated tunability may find potential applications in dynamic functional THz devices.