The inaccuracy of the most widely used potentials in calculating the phonon transport of sp3 carbon materials hinders the use of molecular dynamics simulations for revealing the underlying mechanism of phonon transport in diamond and related materials. Here, we introduce an optimized Tersoff potential by optimizing the parameters to fit the experimentally determined phonon dispersion in diamond along the high-symmetry directions. Molecular dynamics simulations are performed using this new potential to investigate the phonon thermal transport in flawless and nanotwinned diamond. The simulation results show that while the phonon lifetimes of nanotwinned diamond are slightly lower than those of the flawless one, the phonon group velocities of nanotwinned diamond are obviously lower than those of diamond. The present results indicate that the twin boundaries in diamond are ineffective in scattering the phonons and the lower thermal conductivity of the nanotwinned diamond mainly originates from the lower group velocities due to its reduced structural rigidity.