We perform the dispersion-corrected first-principles calculations of vibrational absorption and the far-infrared (terahertz) spectroscopic experiments at different temperature to examine the effect of weak-hydrogen-bond network on the low-frequency vibrations of solid-state salicylic acid. By dispersion correction, calculated frequencies improve especially in the intermonomer torsion and interdimer translational modes which are closely related to the weak hydrogen bonds. The calculated frequencies and their relative intensities reproduce the observed spectrum in the accuracy of 10 cm鈭? or less. Weak-hydrogen-bond network causes a large frequency shift of out-of-plane intermonomer modes and enhances interdimer translational modes accompanied by the O鈰疕 stretching vibrations.