A laser supercontinuum is generated by cross-phase modulation (XPM) driven by an intense terahertz (THz) field in organic crystal OHQ-N2S. In this highly nonlinear medium, the THz electric field induces a time-varying optical phase modulation, which causes a spectacular spectral broadening and shifting of a co-propagating near-infrared laser pulse. The effect is enabled by the large electro-optic coefficient, the low absorption, and the good velocity matching between the laser and the THz pulse over the OHQ-N2S crystal thickness. The XPM occurs when the THz field is aligned along the polar axis of the OHQ-N2S. The results display a promising pathway for ultrafast control of the spectral and temporal properties of laser pulses using THz stimuli.