We have observed strong phase-matched (PM) quadrupole optical second-harmonic generation (SHG) from nematic liquid crystals that possess inversion symmetry. PM conditions were achieved for two configurations by voltage control of the molecular orientation and thus of the refractive indices. Quadrupole SHG was separated from electric-field-induced dipole-type SHG with the help of time-gated measurements in a pulsed electric field.