This study has conducted parallel simulations of interacting inertial particles in statistically-steady isotropic turbulence using a newly-developed efficient parallel simulation code. Flow is computed with a fourth-order finite-difference method and particles are tracked with the Lagrangian method. A binary-based superposition method has been developed and implemented in the code in order to investigate the hydrodynamic interaction among many particles. The code adopts an MPI library for a distributed-memory parallelization and is designed to minimize the MPI communication, which leads to a high parallel performance. The code has been run to obtain collision statistics of a monodisperse system with St = 0.4 particles, where St is the Stokes number representing the particle relaxation time relative to the Kolmogorov time. The attained Taylor-microscale based Reynolds number RλRλ ranges from 54.9 to 527. The largest simulation computed the flow on 20003 grids and 10003 (one billion) particles. Numerical results have shown that the collision kernel increases for RλRλ<100 then decreases as RλRλ increases. This Reynolds dependency is attributed to that of the radial distribution function at contact, which measures the contribution of particle clustering to the collision kernel. The results have also shown that the hydrodynamic interaction for St = 0.4 particles decreases both the radial relative velocity and radial distribution function at contact, leading the collision efficiency less than unity. The collision efficiency increases from 0.65 to 0.75 as RλRλ increases for RλRλ<200 and then saturates.