Properties of covalent liquids under high pressures have been investigated by means of ab initio molecular dynamics simulations. From our simulation, it is found that liquid B2O3 has anomalous diffusion properties under high pressure. We clarified atomic diffusion mechanisms which are origins of the anomalous diffusion properties. We have also investigated metallization of liquid Se under high pressure. Our simulation revealed that a covalentlike interaction exists even in the metallic state of liquid Se, which gives a singular feature of the static structure in metallic state of liquid Se. In addition to these liquids, we have investigated atomic diffusion in basaltic melt under pressure and discussed the mechanism of accumulation in interior of the Earth, in which seismic discontinuity is observed.