We numerically investigate the hydrodynamic interaction of swimming organisms at small to intermediate Reynolds number regimes, i.e. Re ∼O(0.1-100), where inertial effects are important. The hydrodynamic interaction of swimming organisms in this regime is significantly different from the Stokes regime for microorganisms, as well as the high Reynolds number flows for fish and birds, which involves strong flow separation and detached vortex structures. Using an archetypal swimmer model, called "squirmer", we find that the inertial effects change the contact time and dispersion dynamics of a pair of pusher swimmers, and trigger hydrodynamic attraction for two pullers. These results are potentially important in investigating predator-prey interactions, sexual reproduction, encounter rate of marine organisms such as copepods, ctenophora, and larvae.