The penetration of time-dependant resonant magnetic perturbations (RMPs) is numerically studied by means of reduced magnetohydrodynamic simulations, taking into account the neoclassical poloidal viscosity (NPV) damping. It is found that with the increase of the RMP growth rate, the scalings of penetration threshold on resistivity as well as viscosity are significantly weakened in both viscoresistive and resistive-inertial regimes. In the high neoclassical viscosity regime, the scalings on neoclassical viscosity νnc are numerically obtained in the cases of different RMP growth rate and viscosity ν. In the low neoclassical viscosity regime, νnc almost has no effect on penetration threshold, which is unlike ν. Moreover, the synergistic effect of both νnc and ν on the threshold is discussed as well. Finally, the role of the NPV in the torque balance is analysed. It is shown that the NPV tends to restore the velocity profile in the vicinity of the rational surface.