We investigate the dynamical evolution of compact young star clusters (CYCs) near the Galactic center (GC) using Aarseth's Nbody6 codes. The relatively small number of stars in the cluster (5,000-20,000) makes real-number N-body simulations for these clusters feasible on current workstations. Using Fokker-Planck (F-P) models, Kim, Morris, & Lee (1999) have made a survey of cluster lifetimes for various initial conditions, and have found that clusters with a mass \lsim 2 * 104 \msun evaporate in 10 Myr. These results were, however, to be confirmed by N-body simulations because some extreme cluster conditions, such as strong tidal forces and a large stellar mass range participating in the dynamical evolution, might violate assumptions made in F-P models. Here we find that, in most cases, the CYC lifetimes of previous F-P calculations are 5-30 % shorter than those from the present N-body simulations. The comparison of projected number density profiles and stellar mass functions between N-body simulations and HST/NICMOS observations by Figer et al. (1999) suggests that the current tidal radius of the Arches cluster is 1.0 pc, and the following parameters for the initial conditions of that cluster: total mass of 2 * 104 \msun and mass function slope for intermediate-to-massive stars of 1.75 (the Salpeter function has 2.35). We also find that the lower stellar mass limit, the presence of primordial binaries, the amount of initial mass segregation, and the choice of initial density profile (King or Plummer models) do not significantly affect the dynamical evolution of CYCs.