A tunable narrowband terahertz absorber is proposed based on the photosensitive characteristics of silicon. When silicon is insulating without the pump beam, the absorber realizes three-frequency absorption at 0.731 THz, 1.145 THz, and 1.546 THz with absorptivity of 99.43%, 99.99%, and 99.98%, respectively. When the silicon is excited by the pump beam, it is conducting, and the absorber realizes double-frequency absorption at 0.852 THz, 1.536 THz, with 99.99% and 99.31%. The impedance matching theory explains the perfect absorption, and the electric field and surface current distributions are further discussed to elaborate the physical mechanisms. In addition, the effect of geometric parameters on the absorptivity is discussed. The absorber exhibits wide-angle absorption characteristics when light is polarized along the y-direction, and the absorptivity exhibits weak dependence on the polarization angle. The proposed absorber has promising applications in electromagnetic cloaking, narrow-band thermal radiation, and optoelectronic detection.