A method to achieve the region of thermodynamic stability of diamond is described. Pressures in the range 10-30 GPa and temperatures in the range 2000-4000 K may be obtained by current pulse heating of a special graphite-containing sample. Numerical modeling of some regimes of capacitor bank discharge through the sample showed that this is possible by current pulses with a duration 2-10 mus and a magnitude of about 1 MA and higher. In doing so, the conductivity of the sample is of great importance. The analysis of numerical modeling results indicates that the best values of diamond synthesis parameters are achieved for metallic samples. Nonporous material containing small graphite particles having a size in the range of 10-100 mum was used. The best results are achieved when graphite constitutes no more than about 30% by volume of the sample. The method was tested under laboratory conditions. In these experiments, hexagonal diamond particles were obtained. The mean size of diamond crystallites was about 0.1-0.2 mum or smaller.