Ferroelectrics at GHz frequencies has been studied for a long time and already lot of devices that operate in this frequency range are commercially available [1]. THz range starts to be exploited only recently, when new techniques appeared to generate strong ultrashort (single-cycle) THz pulses providing electric field with strength more than tens of MV/cm [2].     The study of the ferroelectric dynamic response to the impact of intensive short terahertz pulses requires the application of appropriate techniques that are sensitive to the processes induced by an electric field pulse. Optical second harmonic generation (SHG) is a powerful method for the research due to its high sensitivity to polarization switching [3].   In centrosymmetric single crystal of strontium titanate SrTiO3 (incipient ferroelectric), the electric dipole contribution to the optical second harmonic generation in the absence of an external electric field is forbidden by the selection rules in electric-dipole approximation. Electric field should breaks the central symmetry of the crystal allowing electric field-induced second harmonic generation.   For coherent control single-cycle THz pulses were used with energies up to 2 J generated by optical rectification in OH1 organic crystal [3]. The crystal was directly pumped by a high-energy Cr:F laser, providing  0.7 mJ, 100 fs pulses with repetition rate of 10 Hz at wavelength of 1.24 m. Correlation function of the pulse is measured by autocorrelator with a Golay cell. It is centered at 1.7 THz with a width of 2 THz.  THz radiation was focused at the SrTiO3 crystal surface at normal incidence creating in the focal point of 400 m in diameter up to 300 kV/cm electric field in the pulse.   For detection of electric field-induced SH signal, the same optical femtosecond pulse was used at 1.24 m, but delayed with the range of 0-300 ps from THz pulse. Synchronously with this pulse, the SHG was measured at 620 nm.   After the exposure of the terahertz pulse (about 1 ps duration) the damped oscillations in the second-harmonic signal were observed. Fourier transformation shows two peaks at 0.5 and 3.4 THz in the frequency spectrum. The last one corresponds to the doubled central frequency of the THz pulse spectrum. The nature of the low-frequency peak is the subject for the further research.   This work was supported by the Russian Science Foundation (contract no. 16-12-10520).