We report on the observation of the giant photoconductance of a quantum point contact (QPC) in the tunneling regime excited by terahertz radiation. Studied QPCs are formed in a GaAs/(Al,Ga)As heterostructure with a high-electron-mobility two-dimensional electron gas. We demonstrate that irradiation of strongly negatively biased QPCs by laser radiation with frequency f=0.69THz and intensity 50mW/cm2 results in two orders of magnitude enhancement of the QPC conductance. The effect increases with the dark conductivity decrease. It is also characterized by a strong polarization dependence and a drastic reduction of the signal by increasing the radiation frequency to 1.63 THz. We demonstrate that all experimental findings can be well explained by the photon-assisted tunneling through the QPC. Corresponding calculations are in good agreement with the experiment.