A numerical study is conducted to examine the flow characteristics of the inkjet print-head with special attentions on the refilling process. By solving the full set of three-dimensional transient Navier-Stokes equations and considering the process of bubble growth and collapse as a movable membrane, it is found that the double refilling channels can reduce the flow surge phenomenon considerably due to the imposed friction. However, for the additional cylinder obstacle placed at the filling channel, the flow surge phenomenon is still present. This is because of the jet-like flow along the cylinder leading to a collision and eruption of fluid angled towards the plane boundary with the presence of cylinder. The calculated results also indicated the flow surge can be moderately suppressed for fluid having larger dynamic viscosity.