A kinetic equation for the turbulent coagulation of particles in a viscous fluid in which the hydrodynamic interaction between colliding particles is taken into account is proposed. The theoretical prediction of the time-dependent behavior of particle concentration is compared with results of experiments in which latex particles in KC1 solutions are coagulated in a stirred tank. It is found that the effect of the hydrodynamic interaction is not negligible, and that changes of particle concentration under various experimental conditions are quantitatively predicted by the present theory. On the other hand, the Saffman-Turner theory is found to overestimate the coagulation rate considerably and to yield a systematic error in the dependence of coagulation rate on the dissipation energy.