We have performed 59Co NQR / NMR measurements on the single-crystalline UCoGe, in order to investigate the relationship between ferromagnetism and superconductivity. The measurements of Knight-shift and nuclear spin-lattice relaxation rate provide clear evidence that both static and dynamic susceptibilities are ferromagnetic with Ising anisotropy. In addition, Hc2 also shows extremely large anisotropy which can not be explained by the GL model with anisotropy of effective mass. These data suggest intimate relationship between Ising magnetization and anisotropic superconductivity in UCoGe.