A phase transition in an organic charge-transfer complex, which originates from the neutral-ionic valence instability, can be tuned toward zero kelvin with use of external pressure or chemical modification as a control parameter. The phase diagram and observed dielectric behaviors are typical of quantum paraelectricity, yet this zero-kelvin transition point namely, the quantum critical point, accompanies large quantum fluctuation of the molecular charge, as demonstrated by the molecular vibrational mode spectra. The result indicates that the pi-electron transfer between donor and acceptor molecules is coupled with the zero-point lattice dynamics around the quantum critical point.