We trace the dynamical evolution of dark matter (DM) content in NGC 6397, one of the native Galactic globular clusters (GCs). The relatively strong tidal field (Galactocentric radius of ~ 6 kpc) and short relaxation timescale (~0.3 Gyr) of the cluster can cause a significant amount of DM particles to evaporate from the cluster in the Hubble time. Thus, the cluster can initially contain a non-negligible amount of DM. Using the most advanced Fokker-Planck (FP) method, we calculate the dynamical evolution of GCs for numerous initial conditions to determine the maximum initial DM content in NGC 6397 that matches the present-day brightness and velocity dispersion profiles of the cluster. We find that the maximum allowed initial DM mass is slightly less than the initial stellar mass in the cluster. Our findings imply that NGC 6397 did not initially contain a significant amount of DM, and is similar to that of NGC 2419, the remotest and the most massive Galactic GC.