Underwater nanosecond-pulsed discharges have been widely utilized in numerous industrial applications. The initial stage of nanosecond-pulsed discharge in water contains extremely abundant physical processes, however, it is still difficult to reveal the details of charge transportation and multiplicative process in liquid within several nanoseconds by currently existing experimental diagnostic techniques. Up to now, the initiation mechanism of underwater nanosecond discharge has been still a puzzle. In this paper, we develop a two-dimensional axially symmetric underwater discharge model of pin-to-plane, and numerically investigate the electrostriction process, cavitation process, and ionization process in water, induced by nanosecond-pulsed voltage. The negative pressure in water caused by tensile ponderomotive force is calculated. The creation of nanoscale cavities (so-called nanopores) in liquid due to negative pressure is modeled by classical nucleation theory with modified nucleation energy barrier. When estimating the temporal development of nanopore radius, a varying hydrostatic pressure is considered to restrain the unlimited expansion of nanopores. We estimate the electron generation rate by the product of the generation rate of incident electrons and the number density of nanopores. The simulation results show that cavitation occurs in liquid within several microns from pin electrode due to the electrostriction, which results in the formation of a large number of nanopores. The expansion of nanopore, caused by electrostrictive pressure on nanopore surface, provides a sufficient acceleration distance for electrons. The impact ionization of water molecules can be triggered by energetic electrons, leading the local liquid to be ionized rapidly. The effects of nanopores on rapid electron generation in water are discussed. Once nanopores are formed, the electrons can be generated in the following ways: 1) Field ionization of water molecules on the nanopore wall continuously provides seed electrons; 2) the seed electrons accelerated in nanopores enter into the liquid and collide with water molecules, resulting in the rapid increase of electrons. It can be inferred that the randomly scattered nanopores act as micro-sources of charges that contribute to the continuing ionization of liquid water in cavitation region near pin electrode. Electrostriction mechanism provides a new perspective for understanding the initiation of nanosecond-pulsed discharge in water.