Hydrodynamic interactions between particle pairs are included in a Lagrangian approach for the simulation of the turbulent dispersion of a discrete particle. Several particles are simultaneously followed, and the set of equations of motion involves a coupling between particles through the use of a resistance matrix pertaining to the sedimentation theory. Results are presented for particle behavior in low turbulence fields, where collisions between particle pairs are assumed to be perfectly elastic. The influence of the turbulence anisotropy is considered and the anisotropy of the particle fluctuating motion is shown to be reduced by collisions.