In this paper, the numerical results concerning different orbits of a 3D axisymmetric non-rotating galactic potential are presented. We use Paczynski's gravitational potential with different birth velocity distributions for the isolated old Neutron Star (NS) population. We note some smooth non-constant segments corresponding to regular orbits as well as the characterization of their chaoticity. This is strongly related to the effect of different kick velocities due to supernovae mass-loss and natal kicks to the newly- formed NS. We further confirm that the dynamical motion of the isolated old NSs in the gravitational field becomes obvious, with some significant diffraction in the symmetry of their orbital characteristics.