We show here the possibility of optical quasi-phase matched secondary harmonic generation in crystal quartz that is a non-ferroelectric crystal. By utilizing a twinning phenomenon, for the first time, we have succeeded in fabricating periodic modulation of the nonlinear coefficient by hot pressing. In this method, stress is applied vertically on a quartz surface. We also devised a special press system. The numbers of twins we have achieved are 10 for 500 μm and 17 for 250 μm periods, and the depth of the twinned area is about 50 μm. Our results suggest that the twinned regions can be controlled artificially, and over a few tens of microns of twinned depth can be realized.